Since you want to avoid political answers lets go to ancient history, and my staple of applying evolutionary theory to every answer I can on this site. Orcs already existed, and us humans beat them (or possibly sexed them up so hard we lost track of who was an human and who was an orc, which still counts as a win in my book!)
The 'orcs' I'm referring to are neanderthals. They were stronger, faster, and more robust then humans. They appeared to have every physical advantage over homo sapiens. They also had some tools and possibly language, but the lessons we can learn from them I believe apply even if we assume your humans & orcs have more complex language and tool use then the various homo-x of yesteryear.
There are two key reasons for why neanderthals did not out compete humans.
They wanted different land then we wanted.
Neanderthals were evolved for the cold northern climate, able to survive comfortably in harsh climates too cold for humans, in fact modern humans got many of the adaptations that allow us to survive in colder climates today from interbreeding with neanderthals (the Caucasians fair skin, freckles, red hair, and even more insulated layering of skin cells all appear to be connected to genes that can be traced back to neanderthals).
However just as homo sapiens were not comfortable in the extreme colds of the north neanderthals were poorly adapted for the warmer climates of the south. It's true a neanderthal would fare better in the southern reaches of homo sapiens territory then a homo sapiens would in the northern reaches of neanderthal territory; but they would still not be well adapted to it. In fact one of the key contributors the extinction of neanderthal was the ending of the ice age and the warming of the northern lands, neanderthals either couldn't survive in the warmer lands or couldn't out compete humans in them; but were get back to that in the next bullet point.
This meant that while homo sapiens and neanderthals did share some regions of the world, allowing interbreeding, there was never any threat of one species being able to completely eradicate the other. Both species inhabited parts of the world the other species was not interested in expanding into, and so there was always areas where one species could safely flourish without concern with competing with the other species.
In regard of your world, I suggest much the same. Have Orcs adapted for a certain territory that they favor so that some human lands are less tempting to them. In fact I'd likely keep the very distinction neanderthals have and have orcs more comfortable in colder northern climates; it makes sense biologically and evolutionary for the sturdier species to be evolved for harsher winter climate. Plus evolution for colder climates would fit for a species that hibernates as you implied your Orcs do.
By making Humans have lands that the orcs consider too warm (or wet, or bright or whatever is counter to their evolutionary niche) you give humans a safe spot to grow and spread that ensure they will never be fully destroyed by orcs even if the orcs could win evolutionary
Of course this implies Orcs could defeat your humans. It may be they couldn't, as neanderthals ultimately proved unable to out-compete humans. And that was because...
Neanderthals ate too much.
It turns out that the big, sturdy frames of neanderthals, that you would think would give them an advantage over humans, was ultimately their downfall. You can't get anything for free, if you want more strength or a bigger, sturdier, frame you need to pay for it somehow, and in this case neanderthals payed for it in calories. They had a higher caloric intake needed to support all those adaptations.
This is a problem because it meant they needed to find more food, more animals to be exact as neanderthals seemed more evolved towards eating meat as their primary calorie source then homo sapiens' more omnivorous diet (which makes sense, meat is a more condensed source of calories which is important if your trying to get as many calories as possible in a day).
Ultimately as temperature's warmed up and Neanderthal's lost their home field advantage in colder climates their real downside was that they couldn't manage to keep up with the higher calorie requirements and effectively the species as a whole starved to death (this is actually an extreme over simplification, another key limit was that they were reliant on meat and thus couldn't adapt to eat increased appearance of vegetation for instance, but oh well).
For your Orcs you can do the same, or something similar. I don't necessarily suggest having their key limit being needing too much food, as that's a more abstract concept that isn't as easy to communicate the limits of to an audience. But the concept of 'you have to pay for your higher strength somehow' still applies.
A species with larger frames and stronger build will also tend towards:
- slower growth and maturity
- fewer children born, and longer length of time rearing children
- (potentially) shorter lifespans
Any of these three reasons can be applied to why humans can keep up militarily with Orcs. Effectively in a battle an Orc soldier may be able to best the average human, but it doesn't matter if the humans can field 1.5 times as many solders as the Orcs can.
From a biological standpoint there is a pretty linear trade off of strength to population in species, so it makes sense that even if humans outnumbered Orcs generally the military strength each species could compete would be roughly equal if we assume they had roughly the same infrastructure/territory. Put another way, X calories worth of food can produce so much fighting strength, rather you dedicate those calories to producing more, weaker, fighting units (humans) or fewer stronger units (Orcs) the same number of calories worth of food is going to support about the same total fighting strength, with a slight favoring towards the humans approach of numbers. That's an extreme over generalization, but the point is that neither strategy has a drastic advantage or would guarantee one species a clear victory in conflict over the other.
Of course conflict isn't limited to war. Conflict can be technological and cultural as well, I'm not going to focus too much on technology, I assume from your question that your intent is to have Orcs intellectually the equal to humans, obviously if they weren't that would be an obvious advantage for humans. I'm not going to even try to make claims over rather homo sapiens or neanderthals were 'smarter'. But culturally homo sapiens may have had an advantage..
Homo Sapiens worked better in a group
Actually before I go any further let me say this is not exactly an indisputable truth, evidence isn't as clear when certain adaptations were made etc. But I'm including this anyways to make my point, it's my answer I can do what I want :P
Neanderthals lived in very small family units, like a pack of wolves pretty much. But comparison it seems humans were (probably?) already moving on to larger 'tribes', much like the packs that chimpanzees and bonobo's lived in. These 'tribes' were still effective familiar units, but larger groupings, think of it as the difference between living with your immediate family and living with your extended family including all your cousins, aunts, and uncles.
This is relevant because humans are very well adapted to working in groups. We survive better with pack behavior, and our adaptions that allow us to survive in large groups, and work together as a group to achieve things individuals could not, may very well have given us an advantage in competition over Neanderthals smaller family units.
Likewise if Orcs were more divided culturally, or even evolutionary, into smaller family units or tribes they may not be able to achieve what a large organized human goverment could achieve.
Of course all this assumes that there is competition. In truth...
Humans didn't fight or kill off Neanderthals
Despite what some like to say Humans didn't 'defeat' neanderthals, they out lasted them. Climate change was the biggest killer of neanderthals. Humans indirectly competed to some degree, in that every resource consumed by humans was one not available to neanderthals, but the common depiction of humans fighting with, out thinking, and dominating neanderthals because humans were just magically better is not how it happened.
Neanderthals and humans lived parallel lives, but they didn't always fight. They got along well for numerous interbreeding episodes to happen, for example. Likely the two sets interacted the way any tribe would, defending their home but just as willing to trade and cooperate as to fight.
likewise there is no need for Orcs to try to take over the world. Look at any nation in the modern world, The borders of Mexico, US, Canada, etc have stayed stable for some time, Most of the time nations accept territory of other nations and trade and negotiate with them instead of going to war. Yes war's and exploration also happens, but my point is that it's not the only option. Part of the reason that one species hasn't wiped out the other is because, on average, neither species sees it worth the fight and so trades and tolerates with the alternate species. They may not like that the species is there, but eradicating them is just too much effort...