If you weren't old enough to understand what was happening when watching the twin towers fall and grasp the gravity of it while it was happening, you're a Zoomer. (And that's a good thing)
Young millennial here. My first memory relating to 9/11 is vaguely being told it was the anniversary of some event that happened the previous year in 2002.
It really wasn't (at least not directly—the aftermath of it certainly was) the big generarion-defining thing Americans like to think it was. The impact on global diplomacy (not least of which is the Iraq and Afghanistan wars), the increased security theatre when travelling on planes. That's certainly a defining generational experience. But the event itself is much less so.