The data I have lists the 1906 as only manufactured from 1906 until 1932. That doesn't mean all were sold then, as some may have sat in stock and were not sold until years later. But all were apparently made by 1932. There are three models with variations of the 3rd model. How to tell them apart is well documented. There are rough serial number ranges by model and also by year for part of their production. But there is a lot of confusion with the serial number ranges by year towards the end though.
22 Short 1st Model 1906-1907 approx range to 113,000
Standard 2nd Model 1908-1932 approx range 113,000-853,000
Expert 3rd Model 1918-1924 approx range is within 535,540-649,951
So an assumption (that actual holds absolutely no water) based on doing the math while also assuming they made the same number of rifles each year from 1925-1932 would put your 1906 around 1929, and it would be a standard model.
Which model and condition has more impact on value than when made IMO.
We had a bunch of the old Winchesters on the ranch I grew up on - the 22 rimfires, lever guns and shotguns. I completely wore out my 1890, a 1903 and an 1906 between about 1953-4 and 1984. Relined the barrel on the 1890 once and on the 1906 twice before they got so loose they had to be retired. Didn't bother with the 1903 as ammo was so scarce and expensive by the late 60's I just retired it. ! shot the 1890 easily twice as much as the others, but it was a much better made model that held up better. Bought a Rossi 62SA clone in 1984 to replace that last 1906, but it never got used beyond one short box of ammo and so still sits new in the box.
They were fun and very reliable little rifles that many folks from my grandparents, parents, mine and my kids generations learned to shoot with.
Anyway, hope this helps you some with an approximate date.
L.