Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
It sounds to me as if you have run into the consequence (or, apparent consequence) of trying a hard reset to factory conditions.
But the Google login demands a Google account that you don't have a password *****
1. the original Google account login is demanded, or
2. the Google account login is needed *before* the data wipe and factory reset is performed.
So I advise you to proceed according to one assumption, then try the other assumption.
Either an 'original' Google account the device was registered to, is needed, or else the current/last Google account registered to it is needed.
How about usernames? try every Google username you've ever used on this phone, or that anyone else (?) ever used on this phone. (And of course, the corresponding password.)
No doubt you have already tried this. But, did anyone own the phone before you? if you bought it from a service provider, take it to the seller or service provider and tell them it doesn't work, and maybe ask for an exchange for another, or a refund, whatever is appropriate to the seller and the exact circumstances that I don't know about.