Phone stuck on "Sign in with a google account that was previously synced on this device"
This is the Device Protection Lock. It started from devices that was pre-installed(Shipped) with Android 5.0(Lollipop) and up.

It's basically asking you to sign in to any Google account that's synced or added to the device.

To verify if your account is synced to your device, please go to Google Dashboard (google.com/dashboard), and sign in with your Google account. Go to Android, then compare if one of the devices listed is the device that is currently locked out. If it is, then you can unlock the device with your Google account. If not, then you need to use another Google account that may be synced to your device. 

If you can't remember your credentials, you can reset your password by going to Google.com/accounts/recovery, but if your change your password before or after Factory Device Reset, you need to wait for 24 hours to sign back on the device and complete the first time setup.

If you still can't get in with the correct Gmail account, waiting 24 hours if you reset your password, then you need to contact the Device Manufacturer for Warranty/Repair options.