There are some pretty large out-of-order issues in the .38 M&P revolvers produced during the Great Depression. Some guns with numbers not far from yours shipped as early as 1930-31, but other guns with nearby numbers did not leave the factory until 1935. You would probably need a factory letter to avoid the approximation problems and get a solid date.
I have two bracketing M&Ps: 544932 shipped in 1927 and 649954 shipped in 1935.