Sounds pre-World War II then. Likely 1930s with a six-digit serial number of 6277XX. It was manufactured at least 20 years prior to the factory's assignment of the Model 10 designation to it's six-shot, fixed sight .38 Special revolver. Its an example of the famous and widely used "Military & Police" that did later become the Model 10.

For your future reference there's a topic category for "S&W Hand Ejectors: 1896 to 1961" which is just the place to inquire about your new revolver. Your revolver will receive more exposure there.

Sure hope to see photos of your new acquisition. Pretty neato that it still has its matching grips.