Google used it internally, that immediately gave it a large artificial boost in terms of a big active foundation and spreading point. It was a big improvement over their earlier work. And it had the Google halo/brand.
I think when you look back at big explosions in tech, it's usually hard to argue it was just some miracle product that was 10x superior to everything else that was the reason (there's usually other competing products or technologies). Often it's a combination of factors that come together and result in the boom (timing, viral cult-like adoptive behavior, etc). Whether we're talking about the web browser (specifically Netscape), the iPhone / mobile Internet, electric car (Tesla), and dozens of other technologies that seem to have followed similar sudden big spikes after seeming to be comparatively stagnant for years or decades (eg solar). They hit that inflection point and off they go. I suspect Google's TF product (along with the other mentioned reasons) was near the sweet spot on timing, combined with a significantly easier to use product, when the GPU was simultaneously getting a lot cheaper and faster. It's likely that for the AI boom to occur, we had to hit a GPU inflection point before it could lift-off fully. Google, as a result of the nature of their business (they perhaps had more reason & resources - due to the nature of search etc - than anyone else to be doing something like TF at that specific time), was there with a product at the right time.
I don't mean to suggest that Google was the sole reason for the AI boom though. Rather, I think the GPU inflection basically guaranteed it was going to happen and Google was in a sweet position out of necessity for the benefit of their own search technology (to their credit they were pursuing this tech despite their money printing monopoly). That they opened up TF, was a big deal though. You can imagine a lot of giants of industry would never in a million years open up something that potentially valuable.