I see as nearly impossible the probability for 2 completely unrelated species to reach huma-like intellectual/technological level in the same time frame.
having subspecies (like neandertal and maybe the homo floresiensis) coexisted in a post-agricultural age maybe is plausible just by having a different geography in an hypothetical alternative earth.
I will make some hypotheses basing of what we know about the evolution of man.
Having more and more differentiated colonizable lands, should reduce the proportion between velocity of migration and velocity of evolution. Thus, for justify completely different species other assumptions are needed, playing with geography, timing and climatic changes.
I can’t tell how much this can be plausible, but should give some possible justification.
This are some characteristic I have though about the general geography and ambient:
bigger planet surface (reducing density of the planet you don’t need to alter the gravity) and/or bigger proportion between lands and oceans.
more climatic zones (you can have that by increasing the planet surface and its rotation speed, i don't know by how much exactly), so you will have more natural barriers like deserts and reduce migrations and exchanges between north and south
more islands, less continents, this can reduce the average height of peoples (so can be like having more lands), also should increase the ecologic diversity trough regions and the probability for communities to remain isolated for long period.
more gravity, this should lead to smaller life forms but also to increase the energetic needs for a similar species of the same size, so i don’t know if it’s usable justification.
weird (for earth standards) ambiental diversification, for example having some common areas with toxic gasses or different air composition (secondary volcanism activity, stratified atmosphere, jungle of venefic-emitter plants…), you can make one population capable of resist in those enviroment (like sherpa can better breath at higher altitude).
lands should be all quite closer to each other even if divided in islands or by others natural barriers. Not only for plot reasons but also because infectious diseases and technology gap. having completely isolated continent will lead one of the two population, once they have meet, to be almost completely wiped out by the one more advanced in trade, urbanization and with more domesticated animals.
So, isolated regions with different climate for help diversification but close enough to make possibile regular but sporadic contacts.
Although we have to consider that for example diseases are considered one possible reason for the extinction of neandertal, so having a single continent probably is not enough for assuming a necessary level of exchange between the two species over the time.
Also, sporadic contacts like trading I assume are more peculiar of post-agricultural civilizations.
Migration and genetic derive are triggered by climatic changes, an overall stable climate through a long time scale should reduce the needs/possibility for migration making more likely for two already separated population to diversificate more, maybe also specializing in some partially different niches.
As far as we know both australopithecus, erectus and sapiens came out from central-east africa. Some hominids follow a separate evolution path in east asia but it seems without much success. The more you are closer to africa the more the phenotypic variation you find in human population, that means we all came from it. Maybe more isolation would have given the asian time to grow in number and become successively more resilient by natural selection.
Thus we can’t know if that can be enough for not being outrunned by sapiens. We have to consider that even small differences can be game changing and different ecosystem can probably lead to different result in evolution.
For example neandertal (that even if derived from african population was more suited for colder climates) actually has bigger brain and stronger muscles, but their anatomy make them consume a more energy than cromagnon, and probably they also lived in less numerous and less specialized groups. Living in more crowded community maybe can have making cromagnon to be more resistant to disease.
More than one Africa
So we can hypnotize a world with at least 1 or more region very similar to the one where the original species has developed. The regions must be well separated by space and natural barriers and should be easy to migrate through them only in some short and specific climatic era.
This way we can hypnotize 2 separated population that became functionally very similar for evolutionary convergence, but are sufficiently genetically separated for having different secondary characteristics (maybe there is no certain way of predict something like that and it can simply be a matter of probability).
You can make things more asymmetric for example making one race significantly more strong and efficient, one more technologically evolved or numerous.
Or one living in more crowded communities and the other with more domesticated animals (or having domesticated animal with which they live in closer contact), so that there is no asymmetric spread of diseases.
We can then create more morphological difference between the two species considering different ethnicities of them and further genetic derive (think about differences inside the homo sapiens sapiens like height differences between pygmies and masai or hemoglobin level of sherpa)
Also we can make very genetically diversificated population meet by having all the continents closely connected east-ovest in a ring-like shape (with some north-south shifting of course).
The first period after the contact should quite obviously be messy, one of the two species should prevail over the other, but you can think to different perfectly plausible ways for creating an equilibrium at some point between the two population, it depends on what are the main advantage of one race over the other.
Having a sufficient large area of colonization with different natural barriers can slow down the spread of diseases, giving the time for evolving resistance to them through selection, and making more plausible for some isolated community to escape the wars.
They eventually have also to evolve culturally and technologically, this would be more relevant the more late in civilization level they meet, were instead physical differences will be less relevant to some extend.
Making the two population meet after agriculture invention can slow down the conquering, if the technological and disease-immunitary gap is not too big.
Nomads groups are more warmonger and needs more lands, sedentary groups have more to lose, can sustain themselves with less land and are less susceptible to climatic changes. Also a better technology level could create to a certain degree a cold war effect, were the consequence of a war start becoming more and more encumbering for civilian activities.
So basically its like making alternative cromagnon and neanderthal meet like after 10bc instead of 40bc, assuming both have reached better technological level.
If the species meet on a city-state/nation/empire level of civilization it's possible that one race will be spared and used for slavery instead of being completely slaughtered.
One race more technologically and disease-immunitary advanced and a race more physically adapted for certain role in an advanced economy (roles that don’t presumably needs the majority of working population, since the second race will probably be in less numbers, differently they will also be considered a potential menace).
For example dwarf that are more suited for mining (shorter, bulkier, better breathing ability in low oxygen environments), a race slightly stronger/resilient/faster for using as mercenaries (a simple more stronger race like giants two time bigger can be considered a menace), a race with smaller fingers for crafting etc…
In the case of more advanced civilizations you have to look for big rivers and mediterranean seas placed in a longitudinally stretched continent as preferred locations for those civilizations.
If the two species are too close so that they can make fertile offspring eventually the disadvantaged of the two will probably be absorbed by the other in few millenniums.
Making them incapable to make fertile offspring can provide continuation of both if an equilibrium is reached.
Lastly we have to consider also cultural/religious mindset, that can lead to more peaceful approach or, like indian caste system, slowing the eventually possible process of hybridization.
So I think this way we can hypothesize, maybe not as plausible but at least as possible, the coexistence of two species/subspecies which live in the same niche, having a shared history only after agriculture invention.
Closely related species that live in different niches can more likely survive, but it's hard to imagine how two species can develop post-agricultural technology and civilization without clashing: with technology humans have colonized all kind of environments, also you can have a species who eat different things but they will likely needs farmable land and freshwater for it. you can think of eating plants that live in different ambient and altitudes but i think it's more likely that the other species will eventually find something to eat almost everywhere or they will domesticate inedible plants or select edible plant that can live there.
Even a single reason for competition can be enough for leading eventually to the destroy of one population.
The closer species to us is the chimp, which actually can be considered rather sapient since they have a very early stone culture from at least some milleniums and can sometimes communicate with us.
Maybe we can imagine a world where an almost-sapient like chimp species is domesticated like dog from wolves. Dogs are quite faster than us and have a very good smell, they are good for tracking wounded prey.
Chimp can more easily stay in higher places, but we also can climb trees quite easily for what we need to do.
They can still have an advantages for hunt in forest if human give them weapons or as scout if they had better sense. So maybe an alternate chimp with stronger senses and better hunt inclination to use like scout can be feasible in dense forest ambients.
Some of them eventually will start to live closer to the advanced race becoming used for others purposes than hunt and eventually learn some of their manufacturing processes. Thus wolves has been domesticated only for 40.000 years, I don’t know if it is enough for making the second species develop a better hand for crafting, speech capabilities and a brain capable of more abstract thinking.
Also the dominating species will probably not want to select those characteristic since making them more powerful they can became a treat.