Yes, the baby is on "Countdown At 6" on that Perrey/Kingsley LP, and that may well be where a lot of people who have used it got it from, but I'm pretty sure that is not the original source, and P & K "sampled" it as well.
The reason I say this is that I used to have this cassette tape when I was a kid with a recording of a sound FX LP. I used this tape for making my own mock radio programs with my two cassette decks and a microphone (ah, those were the days).
On this tape was all your usual usual FX (traffic, sports, fanfares, ambience, nature, battle and so on), including that particular recording of the baby doing its googoo thing, going on for at least a minute or so. Acapella, without music or anything in the background. I remember it very disctincly (especially that "aaaa-aaa"), because I listened to that FX tape a zillion times.
So, I'm guessing it must date back further than the Perry/Kingsley usage which is from around '66. Probably some old BBC late 50s/early 60s type of thing.
Haha, I love these nerdy sample threads. Where's Hawkeye and Easy Mo Bee's hairdryer?