When I swapped an iPhone 11 for an iPhone 13, I had both in my possession to allow for the direct transfer. You have a limited time to get the old phone back to Apple, a week or a bit more if I remember correctly.
You can (and should) backup the old phone with iTunes on a computer (Mac/PC), as a fail-safe then you can restore the new iPhone with that backup to transfer the data. Encrypted backups are preferred as they have more sensitive data in them.