Retrieving data from broken phone

Unfortunately, you are out of luck. You cannot get into a broken phone to retrieve data......and with no backup, you have nothing to restore.

Hopefully, you will set up your new phone to back up automatically each day to avoid a future disaster.

It's too late to worry about losing data which has not been backed up after your iPhone is broken. Backups need to happen before your phone is broken.

The only option you have is to sign into the new iPhone using the same Apple ID as you used on the now broken phone and hope you synced with iCloud. If you did, you can at least turn the switches on for some things on the new phone, which if synced with iCloud will download to the new phone. If you didn't sync with iCloud, you're going to have to start all over on the new phone.

You're welcome and good luck with your new phone!