Can I transfer data from my old phone to my new one after setup

Are you using the same Apple ID?

When using the same Apple ID, any data that you previously had stored in iCloud, will still be available to you on your new phone. If you were using iCloud Photos, then all of your photos will be on your new device. What data are you specifically looking for?

For data that was not stored in iCloud, that is only transferred using the Quick Start method by holding the devices close together or from an iCloud Backup that would contain the data that was not previously stored in iCloud. For example if you were not using iCloud Photos, all of your photos are then stored in the iCloud backup. If you still have your old phone, you can start the process over again to transfer the data using the Quick Start method.