At the risk of disagreeing with your detective work, there's a couple problems with this post.

First, the synthesizer was in use long before this song came out. There are many examples of its use in popular music, going back to the mid-fifties. Even if you're strictly limiting yourself to Western pop music, this isn't in the running, time-wise. The Beatles' Abbey Road, which has Moog all over it (notably in Maxwell's Silver Hammer, where it is clearly audible) was recorded three years prior.

Secondly, and most importantly, that's not a synthesizer in Baba O'Riley. It is an organ, specifically a Lowrey Berkshire Deluxe TBO-1, being key-gated off its own internal drum machine. See the Wikipedia article about this song: https://en.wikipedia.org/wiki/Baba_O'Riley or many other articles that have been written. It is a stellar example of songwriting and technology, but not a synth to be found, sorry to say.

Apologies for bringing this up, but future people will see this, and the information should be at least moderately correct.