Are startups like that? Most of the companies I think of as special in tech were their founders' first startups, not subsequent ones started after a significant cash-out of an earlier one.
That is largely because a.) cash-outs of early startups are often not all that significant and b.) you don't here about those cash-outs.
Microsoft was Bill Gates's second startup with Paul Allen (the first was Traf-O-Data), plus they'd done several consulting projects as teenagers. Apple was the second startup for Steve & Steve; the first was selling blue boxes, and it made enough to finance the Apple I. Facebook was Mark Zuckerburg's third; his second was the Synapse Media Player, which reportedly got a $2M buyout offer from Microsoft.
Generally, you can't plan to be Larry Page, Sergey Brin, Mark Zuckerberg, Bill Gates, etc. Those are the guys who got it right the first time, but there are other models.
Elon Musk is a prominent example of how this alternative pattern works. He founded Zip2 (relatively unknown), then PayPal, then Tesla, and most recently SpaceX.
Evan Williams follows the same pattern. First PyraLabs (again, relatively unknown), then Blogger, then Twitter, now Medium.
In each case like the aforementioned two, you see a relatively small acquisition, followed by an explosion of ability and ambition.
This is the entire foundation of the "PayPal Mafia" - serial entrepreneurs who start out small (or relatively so) and then start serially disrupting greater markets.
Elon Musk is a good counterexample, yeah. That reminds me of one other ex-PayPal person: Russell Simmons founded Yelp after PayPal (though he wasn't a PayPal founder, just an early employee).
I mostly think of the PayPal Mafia as subsequently investors rather than founders, though. Spot-checking another 10 or so of the PayPal alumni, most seem to have gone the angel/VC route post-PayPal, rather than starting new businesses themselves.
