There is a very simple flaw in the "Obamaphone" system that is the root cause of this catch-22 dilemma. I was homeless and had to use an Obamaphone, so I saw first hand how this flaw works.
My solution to this problem was simple: don't use Google. Use Yandex instead because they never require a phone for 2FA and they allow you to set your own custom security questions for account recovery as well as link a backup email account to reset your password. It would be trivial for Google to have these features too, but they won't because this is about spying and tracking and controlling users by forcing everyone to use a SIM card.
The Federal Govt doesn't "give" you a free phone. Cellular carriers give you the phone and the service when you sign up at one of their kiosks usually setup outside local Govt offices that provide services to the homeless. Like the food stamps office.
So you sign up witg T-Mobile or Verizon or smaller carriers nobody has heard of and you get your cheapo off-brand phone with low specs like 1GB of RAM and 3GB of cellular data per month. Great, that is an amazing way to help the homeless since doing everything requires a cell phone now.
But when you sign up, the carriers require you to provide a cirrebtly valid food stamps EBT card and a govt ID like a drivers license with your mailing address on it. They mail a form to that address within 60 days that you must sign and mail back to them to prove you are who you claim to be. I guess this is for fraud detection.
But if you are homeless, then obviously you will never be able to receive that form in the mail to prove you are who you claim to be. Then after 90 days if you have not returned your form in the mail, your free phone service is terminated.
You can immediately go and get a new Obamaphone, but you will have a new number and a new account. There is no way to port your old number because each carrier has totally separate systems to store your account.
This whole Obamaphone program is extremely wasteful because it is intended to help the homeless, but it is implemented to force the homeless to constantly churn through getting new phones every 90 days. I went through several different Obamaphones because of this. Typical Big Govt inefficiency I guess.
It is too bad that Google is so obsessed with spying on people and blibdly trusting SIM cards because you can still use Wifi on an Obamaphone that has been deactivated for cellular service. I don't know why Google refuses to base 2FA on something other than a SIM card. They already control the hardware through Android, so the phone hardware IMEI ID itself should be able to be used as a unique identifier.
Unmoored, trillion dollar megacorporations on autopilot like Google who are managed by multimillionaires Executives living in Silicon Valley and who are staffed by millionaire developers designing these systems of global information control do not think of the use case needs of the poorest, disadvantaged users who fall through the cracks.