The longer it's been since anyone has logged in, the more confidence Google will have that it's really you trying to log in. In all likelihood you'll be able to get back in within a couple weeks.
A few months later it suddenly worked again, and I seized that opportunity to move permanently away from gmail. I was lucky. I do not want my access to my online identity to be governed by luck, however, so really advise anyone who will listen to make the move before this kind of sob story happens to them.
"It won't happen to me" - I thought that too, and no doubt so did the OP. Won't it? How much will it cost you if you're wrong?
It now costs me $50/yr to know it won't happen to me and I'm more than happy to pay a fair price for a good product, like I do for everything else.
The real protection is to get your own domain which Fastmail of course supports, so you can point it at a different email provider if worst comes to worst, like ajross's plausible proposition that:
"[...] I'd put the odds of Fastmail failing entirely as a business rather higher that those of any single user having an unresolvable 2FA glitch with a gmail account. In the world of real data and not anecdata, Big Tech is incredibly reliable."
Well that's funny, because I see a desperate post by a gmail user with an unresolvable 2FA glitch (except by screaming for help on tech-oriented forums hoping someone will notice) basically every week, and yet somehow Fastmail isn't out of business yet. And who knows how many "normies" without an HN/Twitter megaphone just silently lose access, weep a bit and give up?
I have no doubt that Google won't actually lose my email data, but if I can't access it and have no recourse then there's no difference in practise.
I have an alt gmail account that I used less frequently. 3.5 years ago I was abroad right after the first wave of COVID, and logging in from a new laptop (no longer have the old one). When I tried logging in with the correct password, it told me I needed to verify an SMS to an old phone number I haven't used in 10 years (7 at the time I suppose).
Every now and then I'll try logging in hoping they realize that the account is mine, since I have the password, and no one else is logging in (hopefully).
Unfortunately, nothing changes, I still get the requirement to verify with a second device, and I never configured a recovery email for that account.
One day I'm hoping someone will register the old phone number, and I'll be able to smooth talk them into passing the confirmation code to me.
For anyone reading this, do not rely on google services, you'll move cities, change your number, or as OP change your password and _you will get locked out_ with no recourse.