This is one reason why it it would have been good to have automatic backups to iCloud enabled. If you had those enabled, and frequently recharged the phone in a place where it had Wi-Fi Internet access, it might created a fairly recent backup without you lifting a finger. Unfortunately it is too late to enable those now.
Note that if you were synchronizing data to iCloud – e.g., you were using iCloud Photos – that data might still be available from iCloud, for synchronization to a repaired phone or a replacement phone. You can log into the iCloud Web interface ( https://www.icloud.com/ ) even from a device like a Windows PC, ChromeBook, or Android phone. Again, though, this will only help you if synchronization was enabled on the phone before it became damaged.