The age of the Hat is hard to tell. My Father served in the Alpini in 1953 and it is very similar to the one shown, I was told by a dealer that the hat could be WW2 stock that was found after the war and continued to be issued until they ran out. I can not comment on the makers mark on the hat liner as my father took his of his hat to make it more comfortable for wear.
The way the hat is set up it is the type that was sold as a souvenir to Alpini solders that finished national service. The following points are what makes it a souvenir.
1) The Eagle has white (gold when new) thread through out he Cap badge.
2) You have a wovern cord in Red White and Green.
3) You also have a wovern leather cord with stars applied to it. The small star usually represented 1 months service whilst the larger represented the last month of service. I count 14 small and 1 large i.e 15mths service the same amount my father did.
The leather band is also new but that has nothing to do with it being a souvenir. That is a simple replacement.
This type of souvenir hat is still for sale in Italy for around 40 Euro upto 155 Euros depending on rank and branch of service.
I like the hat very much.