You cannot buy a gun from a FFL anywhere in the US without filing out ATF Form 4473.

Here's what Google AI says:

ATF Form 4473 is heavily scrutinized for purchaser legality, both immediately via the National Instant Criminal Background Check System (NICS) and later through auditing. It is the official legal record of a firearm transfer, used to determine if a buyer is prohibited from possessing a gun. FFLs must keep these records for inspection, and lies on the form can lead to federal prosecution.

Key details regarding Form 4473 scrutiny:

Immediate Check: The form initiates a background check through NICS to determine immediate eligibility.

Audit Trail: The ATF regularly inspects these forms at Federal Firearm Licensee (FFL) locations to check for inaccuracies or illegal, straw, or prohibited sales.

Consequences of Falsehoods: Knowingly making false statements on the form, such as on Question 21 regarding prohibited status or the buyer being the actual transferee, is a felony punishable by up to 10 years in prison.

Record Retention: FFLs must maintain these records, which are reviewed for compliance with federal, state, and local laws.

Updated Forms: The form is updated periodically (e.g., in 2022/2023) to improve the efficiency and accuracy of background checks, including specific questions for buyers under 21.

Gun Show laws (limited info):

https://en.wikipedia.org/wiki/Gun_show_loophole

https://www.thoughtco.com/gun-show-laws-by-state-721345