A few years ago, on another forum, someone posted a nice M&P along with the factory letter they had for it. I noticed the serial number was near mine so I wrote it down. According to this guys letter, his gun with serial number C3271xx was shipped on May 24, 1955.
My revolver is s/n C3414xx and is 14,241 revolvers shipped beyond the one in the letter.
If yours is s/n 352000 it would have been shipped 24800 beyond the lettered gun, so the question really becomes, How many revolvers could they make in roughly 6 months. If they could make and ship 4150 guns per month then it is very likely it was made late in 55, in which case it may have not have shipped until early 56.
I have never looked for production numbers but have little doubt that S&W was turning out at LEAST 4150 guns per month, since that is only not even 50,000 per year. If they were turning out 4150 revolvers per month, then mine would have probably been made(shipped) in Aug of 55 and the OP's in late Dec of 55 or early January
Of course this assumes that they could make 4150 of the guns per month that were running with a C prefix at the time, in addition to N and J frames which were in a different sequence, and that there was the same continuous output per month of guns. It seems likely they made the different guns in batches at time, like maybe spend a couple months straight making K frames, then switch to N frames for a period, then J etc. ,, but I am not sure of that. They could have spent the first 6 months of 55 making K frames, then not made another all year long, or had one line making K frames all the time and another line that made N frames sometimes, J frames other times.