What part of Utah? not that it matters, just asking.
The "resident" status is only for college tuition. As with most states residents get subsidized tuition. To get that you have to pay into the state tax system. That takes a year of "residency". That is the only reason a one year residency is required for anything I can think of (maybe hunting permits also).
To your question. I was going to say you will need to wait 30 days. The reason would to get your drivers license changed (you can do that on day 1 I believe). Then you need another form of ID, something with your address on it which is normally car registration or a utility bill (which would take approx 30 days to get) but then I thought "HEY WAIT A MINUTE" that is for a form 4473.
It has been years since I bought a NFA item local, last few years I have been through silencer shop, other vendors, or did my own Form1. I have always done my own paper work and for an NFA item I have never had to show ID to start the paper work. I am 99.9% sure you can start the process the day you move here.
I do have a tip. Always and I mean ALWAYS do your own paper work. The one time I did not It was a 2 year fucking fiasco. Also had a buddy who bought 2 suppressors and he is lazy, dealer had him fill out his part and said he would "take care of the rest". 9 moths latter he get approved for 1, waits a couple months and nothing on the second. He asked me "how long does it take for the 2nd one" I told him that every time I have done multiples I have received them the same day no more than the same week.
He calls the ATF and they have no record of it, he calls the dealer and after some "searching" the dealer found the paper work "behind" a filing cabinet. Buddy had to wait 9 more months for his 2nd can. So he was almost 2 yeas start to finish. My story is WAY more complicated, but along those lines. Once the dealer has your money they could give 2 shits if you ever pick it up. The best part is legally the dealer is still the owner and can use the item all he wants, until he receives approved paper work from the ATF transferring ownership. I know of one story that involves that, clean new can when purchased, can full of carbon 9 months later.
