According to the ATF, non-citizens can purchase firearms.
https://www.atf.gov/firearms/qa/may-aliens-legally-united-states-purchase-firearms
Yup I work with a bunch of H1B types as soon as they get their green cards everyone of them buys a pistol and an AR or 12 gauge for the home front I’m the resident “gun guy” they always come to me knowing I’m former LEO and a pistol instructor / rifle.marksman coach as well. The Indians and the British are both big gun people when they are allowed to be.