back up phone

Backups must be done before they are needed. After is too late. If you have backed up the phone to your computer in the past you should be able to connect it and do it again without having to unlock the phone. And if you had previously enabled automatic iCloud backups the phone would back up overnight when plugged in and connected to Wi-Fi.

If neither of these were set up, and the only phone damage is the front screen, Apple can usually replace the screen without erasing the phone.

Can you access it at all? If it is too damaged, you can’t back it up.