Porting Existing Number to AT&T & Phone Preorders

I am going to be a new AT&T wireless customer and am porting my existing phone number to my new iPhone 13 Pro I ordered from AT&T also. AT&T asked for all of my T-Mobile info to do the port when I was preordering the phone. I'm worried that at the time they ship the new phone they are going to do the port and TMO will cut me off and I'm going to be rendered with no service on my old phone until I get the new one however many days the shipping will take. 

Does AT&T do the porting at the time of shipment or can I initiate it once I am in possession of both phones which would be best so I have no gap in phone service?

Thanks.