Serial # should be on the flats when the gun is opened, also on the barrel and possibly on the inside of the forearm as well.
Seems to have fluid steel barrels, not stub twist or damascus so that would put it somewhere between the later 1900s and WWII.
I have my Grandfather's Ithaca with fluid steel barrels and it is verified bought in 1909. Ithaca made twist barrels after that, so a twist barrel alone isn't a guarantee of the year it was made.
other pics would be helpful