score:4
It's not possible to do Change of Status from the Visa Waiver Program.
It's possible to do Change of Status from B2 visitor status to F1, but the application takes about 5 months to process these days, and you cannot start studying until the Change of Status is approved. So this is probably not going to work for you either.
Exiting and re-entering is the best option for you. If you already have an F1 visa, you can exit your VWP status to Canada or Mexico and immediately re-enter with your F1 visa.