Setting a Default ‘Theme Location’ When Creating a Menu

I’m trying to create a theme which when activated, sets up a primary navigation, adds the homepage to it and then enables it in the correct location.

Here’s what I’ve got so far:

register_nav_menu('Primary', 'Primary Navigation');

$primary_nav_menu_id = wp_create_nav_menu('Primary');

wp_update_nav_menu_item($primary_nav_menu_id, 0, array(
    'menu-item-title' =>  __('Home'),
    'menu-item-classes' => 'home',
    'menu-item-url' => home_url( "https://wordpress.stackexchange.com/" ), 
    'menu-item-status' => 'publish'
));

The above creates the menu, adds a link to the homepage but how would I go about automatically assigning this menu a theme location of ‘Primary Navigation’?

Is this possible?

You need to first collect the menu locations, then set the primary menu location with the menu id.

// Set the menu to primary menu location
$locations = get_theme_mod( 'nav_menu_locations' );
$locations['primary'] = $primary_nav_menu_id;
set_theme_mod ( 'nav_menu_locations', $locations );

Here I assume ‘primary’ is theme location referring to ‘Primary Navigation’.