How long does FAA approval take in non LAANC controlled airspace?

I live within range of a municipal airport and the maps show that I am just inside the controlled airspace, however this area does not use LAANC.

My understanding is that LAANC can issue a flight approval within minutes, but if it has to be authenticated elsewhere, how long can approval take?

If it's a matter of days or longer than I am not even going to worry about it and will just fly elsewhere, and I would like to know before going through the steps of paying the fee, taking the TRUST etc.