Based on your serial number yours was probably late 1947 to early 1948. In 1957 the 38 M&P became the model 10. There definitely should be a serial number on the butt. Other places to find the serial number are the cylinder face, rear of the extractor star and on the yoke and you would have to look through a charge hole to see that one. However, S&W made 927 steel frame Model 39s in the mid 1950s. They didn't assemble or sell any of these until 1966 plus the steel frame Model 39s fall into three different serial number ranges. That is why Smith & Wesson collectors 'never say never' when asked if S&W ever made a certain configuration or variation. I've acquired a Smith and Wesson Model 10 and would like to find out the date of manufacture or shipping date. I'd like to know how old it is. Not 'about' how old it is. It's a Model 10-5 and know that it was made sometime between 62 and 77 but I'd love to when exactly. Jul 21, 2021 Marlin 39a Serial Numbers. Colt Serial Number. Uberti Schofield. Remington Barrel Codes. Taurus Serial Number Lookup. Smith & Wesson Model 52. Smith & Wesson Model 15. Hammerless Revolvers. Sep 24, 2021 The Smith & Wesson Model 10, previously known as the Smith & Wesson.38 Hand Ejector. Serial numbers for the Military & Police ranged from number 1 in the series to 20,975. Most of the early M&P revolvers chambered in.38. World Guns page Smith & Wesson Model 10 at the Internet Movie Firearms Database.Suggested Retail, Dealer Sets Actual Pricing.

I agree with s&wchad, those numbers appear to be restamped for whatever reason.
The s/n will appear on the gun in other places, but the prefix may not be on those other places.
You can look at the inside of the right grip panel to see what is stamped there (assuming the grips are original). Also, push the extractor star all the way out, as if you are ejecting spent shells, and look at the underside surface of the star, there should be a number there.
The problem with these later guns is that they may have the prefix imbedded within the s/n (example 5D12345), is that in the places - other than the butt - you may see these number show us as 512345, especially the grips, they normally didn't stamp the alpha letter, either as a prefix or imbedded number.
The older the gun, the possiblity exists for the s/n to appear in more places, for instance on the underside of the barrel (the flat area that is covered from view if the cylinder is closed, swing out the cylinder and look there, I doubt this gun has it there, it appears too late), also check the crane, on the surface that faces the cylinder, you may need to look through the cylinder with a flashlight to see it, or dissassembly may be required.
Good luck
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