If a company is heading towards an IPO, they MUST already have a CFO in place, probably 3-5 years in advance.
IPOs: Top Signs a Company is NOT Ready to Go Public
While there are financial systems required, there are practices, reports, etc etc that require day after day, month after month, and quarter after quarter monitoring. It's not something that can just be "cleaned up" at the last minute.
Profitability is not a hard requirement but certainly helps.
The "magic number" used to be $100MM ARR but that doesn't appear to be the case anymore.
I'd wager this is in part because of the increased private/VC valuations the last few years.
Strong growth is good. Strong growth among the more profitable product lines is even better.
Margins should be high, potentially increasing as the cost of delivering the product goes down. If the team can put $X into Sales and Marketing and get 3-5X revenue out, that's a good sign.
If you can determine LTV, CAC, and churn, those are GREAT indicators but unless you're senior management, odds are you won't see those.
Regardless, it is NOT something you can bet on because even if it does happen, it can be YEARS down the line and if you're an insider, there are complex rules on when you can do or say what.