This is just not really true. Shared hosting and leased servers were widely available from dozens of providers and very popular back in 2002 when AWS started. Also, FOSS operating systems were very popular for servers back then as well. Sure, bigger players owned lots of servers they sourced from the bigger vendors, but smaller players and upstarts largely did not (and certainly didn't need to).
You are correct. Somehow my brain transported the launch of EC2 back to around 2000. I _think_ I was conflating it with a similar service that was provided by a company I worked for a the time. Since we were doing on-demand machine provisioning then, I guess over the years my brain has assumed Amazon must have been too. fwiw EC2 wasn't launched as a beta until 2006.