It wouldn't be a Model 36 at that SN, but a pre-Model 36 (specifically what is called a Chiefs Special "Baby Chief.") I list SN 336xx as shipping in 6/53. Model numbering did not start until the late 1950s. You may or may not have one of those - a picture would help.
The number you were quoted is probably from the frame under where the barrel threads into it, which is not the SN. It is on the flat bottom of the grip frame, as noted here:
If the SN on the butt is 332X1 and it is a J-frame, and if its condition is respectable, you might want to develop some interest. Baby Chiefs have fairly high collectibility, as they are early versions of the Chiefs Special, and not many of them were made.