First, an apology. My memory was wrong about the 1960s. I have turned up another family piece that I know was bought new in 1965. It is marked 925 (i.e. strerling standard) and THAILAND. I have also checked further and established that the items marked SIAM were bought in 1950 or 1951, not so long after the country's name change when a time lag in changing marking practice would not be surprising (or a delay between making the items and their sale to a customer in another country).
Your boxes are the sort of thing that is made for export or the tourist trade and the use of the term "made in .." places them in the 20th century and probably after WW1. It seems to me you cannot get much further than saying they were probably made somewhere between c.1920 and c.1950 but probably not in the 1939 -45 period when WW2 would have limited the scope for tourism or luxury exports, quite apart from the temporary adoption of Thailand as the country's name during that period as well.