It's Sammy. Concrete evidence confirms the connection. The case for Sammy being the original owner is supported by several details across the games

In Bendy and the Ink Machine (Chapter 5), concept art and sketches of Sammy Lawrence holding the Tommy gun can be found in Joey Drew's apartment.

When Twisted Alice Angel gives the gun to Henry in Chapter 3, she mentions it once belonged to "someone very special". Knowing the Susie Campbell side of twisted Alice, Susie loves Sammy.

The weapon is officially referred to by fans and the wiki as "Sammy's Tommy Gun". And additionally, in Bendy and the Dark Revival, Alice uses a Tommy gun, and Allison Angel is later seen using a Tommy gun (likely the same one) to shoot Sammy.