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It has certainly happened. We know of stars that are younger than humans.
But has someone directly observed this happening? Well, it depends. As already noted, star formation takes a long time. It's not like dark, cold dust suddenly collapses and ignites into a star. During the formation process, the dust is compressed, and as you might recall, as volume decreases on a mass, pressure and temperature increase. As it heats up, it starts emitting radiation. So it's possible to observe this even before becoming a true main sequence star. And we have definitely observed a lot of those, and if you go outside and point your sufficiently powerful telescope in the right direction, you too can see one with your own eyes!
https://astronomy.stackexchange.com/questions/49792/has-the-birth-of-a-new-star-ever-been-observed-scientifically-speaking