In this case, I think it's worth unpacking the term 'startup'. In most of the world, 'startup' has become a sexy synonym for 'new business' and new restaurants are startups and a fellow with a lawn mower and a pickup truck and a trailer is running a lawn care startup...because of the success of startups from Silicon Valley, 'startup' is sexy.
And Silicon Valley is where the other meaning of 'startup' is common. There a startup is a company that is designed to grow fast and organized to receive venture capital and either succeed or fail within the timelines of Venture Capital investors and according to how Venture Capital Investors define success. They define success as valuations in the 100's of millions of dollars.
This means that startups in the Silicon Valley sense usually burn through money in pursuit of growth and usually don't achieve the growth and die and that's pretty much accepted and acceptable by Venture Capital Investors. Startups in the 'rest of the world sense' are not expected to grow-or-fail. They are expected to return reasonable profits over a sustained period and that's what investors in those companies expect.
This means that taking a job at any startup in the Silicon Valley sense should be accompanied with a healthy expectation that the company will run out of money and fail because that's just what happens and with the hope that the company will hit it big and the equity won't be worthless and that's mostly a matter of luck (there's a well respected HN'er who sold their Sun stock and spent it on a Camero not long before Sun went public and the stock would have been worth many times more).
The question I'd ask myself looking into this type of situation is 'What happened to the previous CTO and if there wasn't one, why the hell not?"
Good luck.
You should replace the CFO by a monthly spreadsheet.