@sj from what I’ve determined here and elsewhere, you may be out of luck as far as expediting the process – I do not BELIEVE you can fast-track a 1sst Adult Passport application, only a renewal, you should probably look for & read any posts here about “Fast Track” or “Upgraded” service for more details, or more exactly, call the main HMPO phone #, and at the first prompt, select “8” for “Anything Else”, and at the next prompt also select “anything else” – my experience is that this is the fastest way to get to somebody who may be able to help. Anything else you see here is for all of us largely second-hand/speculation.
Good Luck!