More widely Cold CO2 from dry ice or pressurized tanks is a problem because it’s both releasing a lot of CO2 and that CO2 is very cold which means it sinks quickly. On the other hand babies breath is both fairly slow and has a relatively low CO2 concentration which makes it easier to mix with the air. On top of this breath is warm so combined with a convection current from body heat in otherwise still air it has a tendency to rise which improves mixing.

An extreme version of this happens when a baby or small child falls down a pipe and can avoid suffocating for hours.

The relative differences in weight/density between CO2, nitrogen, and oxygen just aren't big enough to matter much compared to the other forces that mix room air: convection, currents from forced air HVAC, air leakage, etc.

Air is already 80% nitrogen, and when we exhale we only drop the % of oxygen from 20% to 16%. And consider the fairly small lung volume of the kind of infant who would be sleeping in the box.

I'm sure you could get CO2 buildup in the box in very controlled lab settings, but in general practice as a crib it doesn't seem to be an issue.

And in case you were wondering about the general case: is CO2 buildup an issue for infants? The answer seems to just be: no, and it doesn't even depend much on how much you run your HVAC or if you have a fan or how hole-y your crib is, etc. Room air just mixes enough normally that it's not that big of a deal.