The closest SN I have listed to yours is 59043 which shipped in December 1913. There is no way to determine its manufacture date, only the shipment date. That would require a historical letter ($100). It is highly probable yours was manufactured in 1912 or 1913 (at the latest) based on other SNs on my list.
If all you want is the date you could join the SWCA for $60 for a year and Dr. Roy Jinks will tell you the month and year of any S&W handgun for free. Cheaper than one letter and you could get all your S&Ws dated.
Welcome to the Forum. It would be nice to see the gun you are talking about. Some images can often help with narrowing the manufacture date and pictures of the patent dates on the barrel also help. It is near impossible to accurately date a 32-20 since the company did not ship in serial number order. It could be off by years since they just grabbed guns from inventory when orders came in. These guns were also not nearly as popular as the same revolver model in 38 Special caliber. Letter is the only accurate way to get an accurate date.