It's a big mistake to expect to see it in GDP data.
First, there could be very long lags. Again think of what all the applications of relativity are. Needless to say they did not crop up in GDP statistics immediately after 1905.
Second, they are much more likely to impact welfare than GDP. Think of what we like about science and what it does for society. We like that it gives us cooler stuff than we could imagine before with comparable resources applied. It makes our lives better. It does not necessarily make the total amount of money spent on final products higher. Indeed, it may make that lower (think about electronics prices).
So be careful about sloppy talk around STEM externalities.