I found a solution to my problem. I ended up using the wpmu_new_blog
action hook to update the post meta when a new blog is created.
Here is a basic idea of the code used:
add_action('wpmu_new_blog', 'katart_update_new_blog', 10, 2);
function katart_update_new_blog($blog_id,$user_id) {
switch_to_blog($blog_id);
$admin = get_userdata( $user_id );
update_post_meta( 4, 'custom_post_meta', $admin->custom_user_meta );
restore_current_blog();
}
This was a unique situation where I know the post ID. I hope this helps someone.