No you don’t, unless you have a CCW permit but that has it’s own background check that is even more thorough. You have to pass a federal background check anytime you buy a firearm in The United States of America.
Read the article I linked above, she got denied. I also remember another journalist being denied for having a domestic violence charge (and it wasn’t a felony) on his record. *Found it:
https://www.washingtonexaminer.com/columnist-fails-gun-check-blames-store-owners *
Steven Crowder took two liberal college girls that wanted to buy their first gun to a gun shop to buy a gun and they were totally shocked that they had to do a “federal background check” and even asked “then what is this ‘universal background’ check we keep hearing about?”. Also one of the girls was denied because she wasn’t 21 and wanted to buy a handgun.
https://youtu.be/-l4s901oOUY
The left media makes it sound like you can order guns off the internet and it will just show up on your doorstep and buying a gun is easier than buying cold medicine (because cold medicine is locked up and you have to show I.D to get it).
Many states still allow you to do a private party transfer of a firearm between two citizens but not in a store. My state banned private party transfers last year.