The Girardoni repeating air rifle predates the ratification of the constitution by ~11 years and was taken on the Lewis and Clark expedition ~13 years later. Really the whole discussion around 2A is usually nonsense because it ignores the context that the entire Bill of Rights had a completely different meaning prior to the 14th amendment leading to incorporation over the last century (and other expansions of federal power via commerce clause); that is, the Bill of Rights originally did not apply to the states.

Very obviously individuals were expected to be part of the militia, which was the military at the time (c.f. the Militia Acts 2 years after ratification requiring individual gun ownership and very clearly laying out that all able-bodied white male citizens aged 18-45 were part of the militia), but also states could regulate weapons if they wanted.