Can I pick up new iphone without primary account holder?

I have an apple iphone 12 pro max which is currently under the iphone upgrade program. I am not the primary account holder but I do have full access to the account. I am trying to upgrade my phone to be picked up at the apple store using my credit card and all my information, as I have done in previous years when I was using Verizon. I did not have any problems with it before but this is my first year with Tmobile and I don't want to go to the store just to have them tell me I can't pick up my phone. The primary account holder is my father but he cannot pick it up or come with me to pick it up. I am an adult and have been paying for my own phones for years. I am trying to place my order for pick up using the Apple Store app, but it will not let me put my name as the pickup contact. It shows my father's name and underneath that, it says that the phone "can be picked up by the primary account holder or by a person authorized by the account holder." It says to "contact your carrier to verify authorized users." What is the difference between authorized user and full access?

In short, can I pick up my new iphone at the apple store without the primary account holder if I have full access and I am paying with my own credit card?

Thank you in advance for your help.