This isn't true.

Google existed and grew (rapidly) for quite a while before they launched Adwords, which they introduced in 2000. Their growth in '99 was pretty meteoric (prompting a $25M investment from KP and Sequoia) before it rolled out PPC monetization. The Adwords model wasn't new at all-- Goto.com was the first search engine to bet on that model.

Google won because it was a massively better search engine... Not just 10% better-- it was "holy crap" better on a mess of fronts (notably: serving up what you were looking for).

I think that's incorrect, Google worked mostly because it was a better search engine (crawling the web to find major nodes was a brilliant idea), and because it had a clean design.

I disagree with you. Google won because it had and still has a better search and less clutter on the search page.

With a better search experience users came and advertising became a major money maker.

Google beat the other search engines in 1998 because of PageRank and a clean UI. Yes their monetization platform has allowed them to improve their product and dominate the market, but that isn't how they became the search leader initially.