matt, welcome to the forum and congratulations on the purchase of your first firearm...
you're correct in that firearms and munitions must be shipped next day. that stated, are you sure the person you purchased the firearm from is in fact a FFL. Now, if the seller is an FFL and failed to inform FEDEX he was shipping a firearm, then there might be a slim chance for a problem if it hits a search.
did you get a tracking number so you can follow your firearm package? other than, wait and ensure an adult is home to sign for your package.