Allow templates to implicitly set in child theme.

I am setting up a large website that requires compartmentalisation. As such I have opted for Multisite with a subdirectory setup.

I have used wp-cli to scaffold a child theme based on hello-elementor and created my default header and footer on the main site with the respective names of default-header and default-footer.

Is it possible to be able to hardcode the theme to fall back to the main sites default header and footer if one has not been set specifically in the subsite or even to force the template parts across all subsites using the same child theme to unify branding?

The idea is to change the header or footer on the main site and all the subsites reflect the change without having to manually go through them all.