Just look up the Bbl Date Code as Alk8944 says.
My 30S Express has that Date Code on the right side of the bbl instead of the usual left side . Right along with the REP proof mark and inspectors marks.
Mine is 'WE' (Aug/1936). For some reason it is marked twice (?)
Second stamping is not a Repair Code date as there is no '3' with it.
I like this Remington Collectors Society website for the codes and dates.
Manufacture Dates – Remington Society of America
A couple of the others on the web have small errors in the Yr/ date codes.
Nice rifles, though heavy by todays 'sporter' standards. Most everything from that era likely is.
Makes for very comfortable shooting!
Added:
I 'Think" this is a page for the Model 30 from the Rem factory serial number record books.
It's not the full listing of course from the start of production around 1920 and forward. But it seems to indicate Month to Month ser# production.
Some Months are broken down into Weekly production.
The page begins in the first week of Jan/1927 ending (Starting?) with ser# 7719
The next entry is for Feb/1927. Ending (Starting?) Ser# 8025
So I would think your ser# would fall into that first entry somewhere.
Beginning of Jan to end of Feb/ 1927.
This is all an interpretation by me, so take that for what it's worth. I'm not the collector/researcher type.
These are Remington Factory seial # production book copies though and are in the hands of the Remington Collectors Society.
The Bbl Date Code stamped on the bbl is when the finished rifle/shotgun was sent thru the Range at the factory for Proofing and final inspection.
That Bbl Date Code can be different than the Ser# production record book. The ser# being rolled on and then recorded during the mfg process and usually done in the metal finishing & polishing 'room'.
Long before the finished product ever gets to the range especially if the bare unfinished parts are shelved for lack of demand, they could sit for some time.