The FDIC should take on the bills and loans, and pay out the cash now. They will collect the entire balance eventually and they have the benefit of time and I imagine they’re authorised to hold assets like this long-term (or do a cash swap with the fed, they have plenty of long term bonds what’s another $100B). I have always assumed this is what the whole point of the FDIC and similar schemes in other countries. They foot the bill immediately and then spend time fixing up the mess but eventually reclaim it all back. It’s a bit like if you’re not at fault for an accident - the insurer pays you out now and then they deal with the at-fault driver and you’re not involved in that process afterwards in most cases.
According to the press release, SVB had $206B in assets and $176B in deposits. The math is simple: everyone should get their money back. There may even be some money left over for investors.