The tree would have grown around the barrel in less than 20 years.
The weathered stock is the best indication of how long it has been outside. It looks like is has been exposed to the elements for a very long time. The metal parts look the same, weathered to a patina rust.
This gun looks much the same as many wooden and/or metal things I've come across hiking in the deserts of the west where I grew up and lived for four decades. This is a believable find.
Maybe not. Desert conditions, hot and dry. snow covered in winter. Trees grow at different rates. We’ve got stands of Port Orford cedar to the south at the highest point of elevation in the county. I’ noticed the scorch marks on the bark many times, but it toolk me awhile to ask a friend when the area burned. He said it was the late ‘’60’s. Fifty years later and they still retained burnt bark.