HTTP protocol has been in use by the Web since 1990, HTML, as standard, since 1996.
The web browsers explosion started with 1993's Mosaic.
According to the US patent office, Gary Kremen is the primary inventor of a patent for creating dynamic web pages, patent #5706434 which he resold for over $1,250,000 see - http://www.mikeford.com/?m=200702.
For server-side dynamic pages:

The dynamic page generation was made possible by the Common Gateway Interface, stable in 1993.
Then Server Side Includes pointed a more direct way to deal with server-side scripts, at the web servers.
For client-side:

The first "widespread used" version of javascript was 1996 (with Netscape 3 an ECMAscript standard).