Adding a Page Using a Plugin

Background: I’m new to WordPress but have been developing on PHP for over 10 years.

I’d like to know if there’s any way to register a “page” from within a plugin but without adding a page to the database and without adding a template file to the theme.

I’m writing a plugin and I would like it to be possible to simply enable the plugin (without copying files to your theme folder and without adding a page in the database) to get it working.