But if Berners-Lee hadn't started the WWW, someone else probably would have within a few years: the hard part was the development of the internet, i.e., a flexible low-cost wide-area network where anyone could start a new service (look in /etc/services to see all the services that people have defined over the years) without the need to get permission from anyone.
IIRC the first WWW server went live in 1990. By then there was already WAIS, Archie and Veronica (search engines for anonymous-FTP sites). In 1991, the first Gopher server went live. Gopher grew rapidly till the late 1990s.
The US government's Advanced Research Projects Agency started funding research into "packet-switched networks" in 1960 which would eventually lead to the internet, which went live in 1969 (under the name ARPAnet, but only a pedant would say that ARPAnet is not the early verion of the internet). Then the USG continued to fund the internet every year till it no longer needed funding in the early 1990s.
So, CERN and Berners-Lee (mostly the latter because no one at CERN other than Berners-Lee cared much about the WWW in its early days before it became a big hit) get some credit for the WWW, but in my reckoning it is a small amount of credit.