An expression w/Math and Rand() won't work, since a random number will be generated for each and every track. You're hoping for one random number generated, and then all tracks matched against that.
Instead, you want to use the built-in smartlist search and modifier operations.
[Media Type]=[Audio] [Date (year)]=1930-1963 ~limit=1,-1,[Year] ~sort=Random
You can use the search/smartlist wizard to build these. This one says, select only Audio, the Year must be within your range of 1930-1963, limit to only 1 year with all files (-1) from that year, and sort randomly.