They also didn't have much in the way of worthy competition. That really helped them out a lot. It's different now. So much saturation in many areas things have moved from the era of bold ideas to the era of carving out niches.
Was it 'worthy competition'? Hard to say without hindsight bias (only the winners 10 years later were 'worthy'), but I doubt Mark Zuckerberg or the Google founders felt there was no worthy competition. It seems fairly clear to me that Facebook (and Google) succeeded because they made better decisions (on average) at a gazillion small decision points, not because they had some great idea that no-one else had thought of.
Friendster and Myspace were the big players for Facebook, Lycos, AltaVista, and HotBot were competitors for Google. A new social network or search engine didn't get noticed back then.