Please consider that, YES, someone can "just start getting 100s of spam [e]mails" without signing up for anything new or providing an email address to a list or anything else. All it takes is for your email address to be involved with a breach, and on a dark web list that was sold.
I know this is a little bit of an old post, but the best way to block spam mail is at the provider level (as mentioned by others). Most common email service (gmail, outlook.com) offer junk mail options that can be turned up to the point that only your contacts will make it to your inbox, and everything else will go to junk.
As mentioned by others, most email services will allow you to use aliases that you can then redirect to a different folder, so you don't need to give out your "real" email address when you are required to use your email to sign up for something. This will give you better flexibility to block things that are unwanted later.
