Hi Alex and welcome. I've never gone more than 3 days in over 30 years. Just give them a call to inquire. I have literally showed up at my FFL an hour after tracking delivery and picked up my firearm. They do have to log firearm into their inventory for ATF tracking but a week is excessive. Cheers, stay safe and good luck!

a week is not good my ffl receives the gun logs it in then calls me. I would call the FFL that you shipped it to and arrange a time to pick it up

Hi Alex, if it's been a week, I would call the shop and ask when I can come in and do the paperwork. (a week is way too long)
Most FFL's will call you, some will not, others just take their good old time.
A tip, when using a new FFL, give them a call before ordering and ask what their procedures (and costs) are so there will be no surprises later.
Good luck!