Social icons in submenu of navigation block

If you will use font based icons it can be done with CSS alone. Use your browser’s element inspector tool on the icons in the WP admin menu for an example using dashicons font. The :before pseudo-element is used to place the icon with CSS.

Thank you bcworkz. I can certainly use the dashicons font. However, it would be nice if the social icons “block” could also fit within a submenu.

I hear you, but AFAIK there’s no way to nest any block within the submenu element. If you like, you could raise the issue in Gutenberg’s GitHub project suggesting such a feature be added. There’s no guarantee anything would be done, but it could pique someone’s interest enough to pursue further.