You can build a site of your own without using a single framework.
But, the thing is even if you don't use one, you end up writing one for yourself, maybe even a tiny one to better manage your code.
I don't know that if you can call this little piece of code "a framework", but maybe something like a "micro framework" (something like preact, hyperHTML, lit-html).
You don't, actually, most sites are discovered organically through links on other sites. Submitting links hasn't been common since the days of Yahoo and DMOZ.
You're right that "consent" is the important legal issue, but it's usually implied based on what your site requires re: authentication/authorization, robots.txt, and the controls Google has provided to let you tell them not to index a site.