Upgrading iPhone Model

Moving from 13Pro to a 15Pro.

Can I use my most recent back-up (to my M3 MBP) to bring a new iPhone into my life rather than have the carrier agent do the transfer before I walk out of the store?

I'm uncomfortable leaving sensitive data with someone I don't know even though I'm doing business with their company.

I've done this more than once before but on my lonesome, after 'trading in' my previous iPhone, the difference being I had the new one and the old in my hands during the transfer.

All thoughts welcome!