They started stamping made in USA some time in the 20’s I’m not sure if it’s true for all makers but if you had a Winchester I’d say teens or 20’s. The one that just says gauge may be older.
Fly boy baby sitter that was me, loved every minute of my job....Spent the majority of my career working MC-130's. There was an EC-130 unit out of DM (41st, 42nd or 43rd can't remember CRS setting in) with us at Masirah Island after 9-11, along with the ones out of Harrisburg PA (193rd SOS).
Worked the C-130J's and WC-130J's out of Keesler for 10 months with the Reserves.
Having owned many shotguns... I was not familiar with the 16 gauge.
Research shows that the first manufacturer of this model was:
"John M. Browning
The Model 30 and 31 were actually the Savage Stevens 520/620 pump action shotgun was designed by John M. Browning. They were first introduced in 1904 and were sold with the Stevens name and also rebranded for the major catalog retailers like Montgomery Ward's Western Field line."
Browning Shotguns are by far my favorite for their exquisite detail to manufacturing.
The 16 gauge was a gentleman's gun as it would handle most game without the "kick" of the 12 and 10 gauge.
It did decline due to skeet preference.
"The decline may be traced to 1926, when the official rules of skeet declared that only the .410, 28-gauge, 20-gauge and 12-gauge were permissible. As skeet shooting grew in popularity – along with trap, a 12-gauge-only affair – the 16-gauge took a backseat in manufacturers' research and development"
Your 20 Gauge otherwise unbranded might be CIL out of Canada.
16 bore (0.662") was common in the days before cartridges. That is the diameter of a one ounce lead ball ("Gauge" = the number of pure lead balls to the pound). I have a 16 gauge flintlock smoothbore with a 42" barrel that weighs seven pounds on the nose.
It was also the "carbine" bore size for light infantry muskets in the British Army and a lot of officers had personal muskets made in that bore size. (They weren't issued muskets because they were supposed to be strategizing and directing and not participating in battle).