If 27377 is the correct SN (from the bottom of the grip frame), I would guess closer to late 1926 - early 1927. Is it a 2nd or 3rd model (the latter with the ejector rod shroud)?
There are posts here about when heat treatment was modified at S & W but I think it was 1927. Others will be along with more details but only if you post photos .
SN 27377 would put probable shipment as sometime in 1927. The cylinder would have been heat treated at that time. But whether it is or isn't is not an important consideration unless you want to handload some really hot .44 Specials. If it doesn't have the barrel shroud for the extractor rod (and from the SN it probably does not), it is a .44 HE, second model.
S&W .44 Hand Ejector
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Linear Mode
