I did a little research as I do love work buttons...
To answer your question about how old "Big Smith" is take a look at this label
View attachment 1557898 it says "Since 1916"
The design of your button looks much older than the 40's-60's design. I would guess your button from 1916-1930. The star was commonly portrayed on work clothes by many brands in this time period. I think it was a union symbol and these companies were very proud of the standards held by the union garment makers.
check out this guy from back in the day, sporting his Big Smiths
View attachment 1557905