I was 7. I probably built something with Lego that was way cooler than a website.
You can continue that legacy with the open source 3D printing movement that's growing, and potentially continue building things that are way cooler than most web sites.
Nitpick - NCSA Mosaic wasn't the first generally available web browser, Viola was around at least six months before Mosaic.
I'm thinking the person you replied to knows a thing or two about "Awesome" on the web. I'm not sure he was old enough to have done much on or off the web in 1993.
I think Paul was just about to enter college then, so he was old enough. My point is that it was actually quite forward-thinking to try out anything on the web in 1993.