This is a security feature, so it can't be bypassed. If your Google login isn't allowing you back into the phone, then it must have been used when you got it and the last owner didn't sign out properly.
If that's the case, then you'll need to try getting in touch with the last owner to use their login to get through FRP. Once set up, remove their account and factory reset again. That should let you set it up without FRP.