I think there's likely a way to convert fiat to usdc but I don't think there's one where you can link a random user to an exchange without paying a fee (because they'd be providing the same service as you).

There's then the possibility of using systems already in defi like liquidity pools if your hypothetical exchange was considering allowing users to put up funds (on the chance the you didn't have the provisions for it). I'm assuming stripe has an api so you can confirm when a deposit has happened though.

I've been thinking about how an exchange could be made too and I don't think you'd need to "bulk" buy bitcoin necessarily as you could keep an amount of stock and provide for more later on when the initial has been taken - it generally fast to buy bitcoin either otc or via an exchange (otc is especially fast with cash deposits).