The earlist examples of t-shirt type tops appeared in the Sears catalog in 1944. Though these are actully "polo shirts", they still resemble the modern day t-shirt and that can't be denied.
There was a trend in the 1940s of girls wearing their father's or brother's clothes. They would usually pair jeans with an oversided dress shirt and then a flannel coat over that -- setting the groundwork for the 90s "grunge" look! :) Check out these girls in jeans and various oversized men's clothing, all from 1944:
So here is photographic evidence that women did indeed wear jeans and t-shirts in the so-called "Golden Era." Some even purposely looked sloppy while doing it! Others look like they could be plucked from the street today. I know that women *didn't* wear these clothes to school or for going out to nice places, but for play and hanging out with their friends these rebellious duds were perfectly acceptable. So much so that Sears catalogs even cashed in on the trend!