do you have reason to believe none of the two?

Depends if you're talking about "OpenAI, Inc." (non-profit) or "OpenAI Global, LLC" (for profit corporation). They're both under the same umbrella corporation.

The parent is, OpenAI Global, LLC is a for profit non-wholly-owned subsidiary with outside investors; there's also OpenAI LP, which is a for-profit limited partnership with the no profit as general partner, also with outside investors (I thought it was the predecessor of the LLC, but they both seem to have been formed in 2019 and still exist?) OpenAI has for years been a nonprofit shell around a for-profit firm.

EDIT: A somewhat more detailed view of the structure, based on OpenAI’s own description, is at https://news.ycombinator.com/item?id=38312577

A non-profit can make plenty of profit, there just aren't any shareholders.

As someone who is the Treasurer/Secretary of a 501(c)(3) non-profit I can tell you that is it always possible for a non-profit to bring in more revenue than it costs to run the non-profit. You can also pay salaries to people out of your revenue. The IRS has a bunch of educational material for non-profits[1], and a really good guide to maintaining your exemption [2].

[1] https://www.irs.gov/charities-non-profits/publications-for-e...

[2] https://www.irs.gov/pub/irs-pdf/p4221pc.pdf

NFL was a non profit up until 2015ish