President Biden, Cannon for sale, 1799

 9 pounders, 6 pounders, as well as 12, 18 and 24 pounder carronades on sliding carriages; English cannon powder; round shot, double-headed shot and canister for above weapons; also, cutlasses and pikes for close work.

Other ads for same year list cannon.

So, Mr. President, regardless of your wishes on "The way things should have been," in years following adaption of the Constitution, American citizens could buy cannon.

https://gunfreezone.net/it-is-like-the-white-house-does-not-have-access-to-google/