Before I give the answer you're looking for, just a word on atmospheric modelling, particularly in respect to fire. I know you're handwaving it for now, but to explain how it works;
The best way to think of an atmosphere is in terms of Partial Pressure. If you think of 1 ATM being 1 Bar, or the pressure of atmosphere experienced on Earth by someone at sea level experiencing average pressure, then the amount of gases we need to survive are best expressed in terms of partial pressure, not a percentage of pressure. So;
1) Humans need between 0.15 and 0.30 ATM of O2 to survive normally
2) Humans need there to be less than 0.02 ATM of CO2 and other toxic gases to survive
3) You can add inert gases to taste, remembering that Nitrogen isn't truly inert, so you can only add up to around 2.5 ATM of it before it causes a narcotic effect and can potentially cause other issues with long term exposure.
Add up all the PPs you put into your atmosphere, and that gives you the atmospheric pressure on your given planet. The important point to note here is that if your humans are breathing, fire is possible. The PP of O2 required for humans is enough to start fires, regardless of what other gases are in your atmosphere. In other words, PP is what counts, NOT %P.
But for the sake of argument, let's handwave that away and figure out how your proto-humans will fare on your fireless world.
To begin with, most anthropologists believe that humans didn't develop their intelligence significantly until they had harnessed fire. This is despite the fact that they had the capacity for many millennia beforehand. Why? Because before fire, they were purely intent on survival. What fire did was give them a safe place to rest at night, and think. Not about their next meal, or what's out in the darkness, but on what they did during the day, what they saw, what patterns they could form out of their observations and what could have possibly gone better.
On a new world, if they're inherently safe (IE no real predators) this might not be as much a factor but if it's similar in safety to ancient Earth (read as not very) then that ability to sit and think somewhere that natural predators won't approach has been taken from them and that could significantly retard their rate of development as a species.
Fire, when you get right down to it, is used for a lot more than cooking. The Aboriginal people of Australia used to use it to clear out brush before summer, effectively back-burning to prevent firestorms during the heat of summer. That's not a problem on your planet per se, but that lack of burning away means that your forests don't have a mechanism for getting rid of excess humus and other debris, like dead trees. This could cause your proto-humans other issues like providing ideal ambush spots for any predators that do exist, and a problem with rotting vegetation infecting usable fruit and vegetables with various diseases. It also means that you lack a key strategy in protecting yourself and feeling safe, knowing that other animals fear fire. This in turn could lead to other strategic hunting methods (like scaring animals into traps) might not happen either. The other use that it had was in tool forming, it being a tempering agent for certain materials.
Could your humans survive without fire? Like you say, there's already compelling evidence that they did. Would they thrive and grow? Perhaps not. The more you want your humans to advance beyond mere survival the less likely it is to happen without fire.