Imagine you own land that has a parking lot on it. Someone parks their $250k lambo on your land and leaves it there for a few months. You don’t get taxed on that.
You certainly don’t report owning a new $250k lambo, and then later amend your tax return when the owner comes back, that would be a false report.
The conversation would probably go like this:
Dude: "Hey taxman Google sent me money but it's not mine"
IRS: "Ok don't spend it or it becomes income, if it turns out it was yours file an amended return. Contact us and reference this conversation and any penalties will be waived."
The IRS is not extremely accommodating and will not work with someone who is dishonest or evasive about their issues.
Yes, in most cases, government agencies will work with you and behave rationally. But one time in <some large number>, things go a different direction. And the people with the power can turn your life into a nightmare without batting an eyelash.
I would get a lawyer, someone that knows how to best protect you from the system.
Anyway the correct analogy here would be incorrectly receiving from someone you know payment in cash which should have been given to someone else. You realise the mistake when you are back home so you bring it back later. You obviously didn’t owe taxes while you were merely storing the money which wasn’t yours in the first place.