It sounds crazy if you read about the math first. Which almost everyone does ... now. But in the lab, if you set up a detector array that reports individual discrete particles arriving one at a time, that is exactly what you see. You just see random arrival times. You don't see a smooth wavefunction that then collapses.
The problem was never to start with the math and try to understand what's happening to a "wavefunction" or how the heck it could possibly "collapse." Instead they started with the crazy experimental results and made math that seems to always fit so far.