As a start, you probably would have to use a HEPES buffered medium rather than one that uses sodium bicarbonate, as the latter requires CO2 enrichment.
Cell culture needs proper humidity and C02. Therefore, cell culture WITHOUT C02 is likely to initiate a stress response in cultured cells. More importantly, any data from cells will be questionable (and useless).
The reason that mammalian cells are usually cultivated in a 95% air/5% CO2 environment is to maintain (i.e. buffer) the pH of the media via the HCO3 ion. Other buffering systems are available and do work. @Ron has identified one that is popular: HEPES. I suggest that you read the technical notes from Corning, Lonza, Invitrogen, even Sigma (now Merck).
FYI, this question was asked, and answered, previously in 2013: www.researchgate.net/post/No_Co2_incubator-can_anyone_help.
CO2 is old-fashioned, bulky and unnecessary with the right culture device. You do not need supplemental CO2 incubation anymore for your buffered culture media if you grow the cells in the Petaka G3 cell culture cassette. The Petaka G3 automatically and perfectly maintains your media pH levels through its microchannel gas control system. No supplemental CO2 is needed! You also get the benefit of precise, automatic control to physiologic O2 levels (3-7%) versus open air (21%), which is artificial and damaging to many cell types. For the best cell growth just get the Petaka G3 and grow your cultures in a warming incubator or cabinet without any supplemental CO2. Your cultures should do great.
You are less than half correct. I am not "shilling" anything. I provide information in my answers related to an area where I have particular expertise, namely gas control of cell culture. Yes, I encourage people to look at the Petaka because it is amazing technology. Is it my fault that this particular technology solves all of the common problems associated with gas control? What do you want me to do?...I have a special interest in questions about hypoxia and cell culture gas control, and I know a lot of technical solutions, so I provide the best, most scientifically accurate response I know to provide. Would you rather I share responses in areas I am less familiar and intentionally give bad advice? Do you not also give advice in the areas you are most familiar with? Come on. If you had it your way could nobody reply any one technology more than once? Moreover, can you show that any of my responses are not truthful, accurate and appropriate for the question asked?....I claim that my responses are perfectly accurate and appropriate to the question asked. I agree with you that if some salesperson came in blanketing sales messaging in an unsolicited manner, that would be inappropriate. I only reply to those people asking specific questions, with focused, timely and appropriate information. Take this question for example, do YOU know of ANY device other than the Petaka that supports long-term culture outside of a CO2 incubator (400ppm CO2)? I know I don't, and I know you don't either because it doesn't exist...not in bicarb buffered media anyway, and HEPES buffer has major drawbacks as described above. So what would you have me do? This guy has a question and I have knowledge of the only solution out there. Please lighten up...nobody is "shilling" anything. I give advice based on my personal cell culture experience. If I share information about the Petaka its because it is the technology I am most interested in discussing now and because its flat-out amazing.
Of course... please read my post above explaining why this is perfectly fine. You are implying that if a person posts only about one technology or one product that that automatically does not count as bona-fide scientific exchange. I could not disagree with you more for all kinds of reasons, but I respect your right to post whatever you like. I sure like me, you have earned it.