Broken Screen, Locked phone, Not backed up for a year!

My son's iphone 7 has a smashed screen and so unlocking it is impossible as we can't see anything on the screen. We want to transfer the phone to a new handset but realised he's not backed it up for a year so will lose phone numbers, photos and messages etc - disaster for a 13 year old! How do you unlock a phone where you can't see the screen and Siri doesn't work? Thanks