I'm sorry, but this is a classic Catch 22.
You can't use the screen to sign in because it is broken, but even if you could bypass Face ID, you would still be asked to enter your passcode, which you cannot do....because the screen is broken.
The only solution will be to make an appointment at the Apple Store or take the phone to an authorized Apple service shop to have the screen replaced. Then, you can restore the data in your backup back to the phone.
You can find a list of authorized shops in your area using this link: Find Locations
Good luck.