Removing Default Widgets in Sidebar-1

I’m working with multisite and I created a child theme from 2011.
I want that when I create a new site with my own default theme, the new site is set with a personal sidebar I created with my own widgets already loaded.

I managed to create the sidebar in functions.php of 2011-child, and now I would like to remove all the default widgets that populate the first sidebar (which are: search, recent posts, recent comments, archives, categories and meta) so that I can add the ones I want. I believed thes are not tied to the theme but to WP basic source files.

All I managed to do is unregister the widgets, but if I do so they disappear completely from the WP GUI, even from the “available widgets pool”. I just want them out of the first sidebar, and keep them in the available widgets pool.

Where and when are these default widgets put in the first sidebar?