IF you're going to a US Customs office that is INSIDE the terminal building, it MIGHT be a good idea to NOT take your firearm into the terminal in a soft case and be wandering around. A locked hard case like you'd fly with would draw less attention.
When I get them, before trips, I just put the rifles in soft cases and lock them in the trunk and NO ammo. Park in short term parking and then go to the office with my filled out and unsigned 4457. I go in, tell the officer what I want. Sometimes, they just check my ID/DL and have me sign it in front of them. Most of the time if they have the manning, an officer will go to the car with me to confirm serial numbers on the rifles. Try NOT to pull them completely out of the vehicle or the soft case if you can UNLESS the officer SPECIFICALLY tells you to. Most of the time you can just unzip the case and flip the rifle over so the officer can see the numbers. They check/confirm the form info against the rifle(s) and I follow them back to the office.
The firearm info and your ID is run thru the NICS computer to make sure it's not reported as stolen and you don't have any felony convictions. They counter-sign, put the office location number and their stamp on it and you're good to go.
IF you used the downloaded and fillable
HERE , you DON'T need to print the second page. It will normally print out on a full sheet of 8x11 paper but the form itself is just a little larger than your passport. After I get home, I trim off the excess paper and then use 2" wide clear packing tape on both sides to sort of laminate this one and use it as my "master" copy that I carry with me. I make extra copies from it.
I put one copy in my rifle case along with a copy of my passport, invitation letter, airline ticket and temp firearm import document ie. SAPS 520 or Namibia Temp Import Worksheet. I keep the original copies of all this with me. This has helped me get delayed firearms home twice.