How can I copy all users to newly created site on a multisite network in WordPress?

How to add user to blog?

You can use add_user_to_blog function to do that. After Codex, it:

Grants the specified user permissions of the specified role on the specified blog.

And you use it like so:

add_user_to_blog($blog_id, $user_id, $role);

How to do it automatically?

You want to do this automatically, when new site is created, so you’ll have to write some code and use wpmu_new_blog hook.

Here’s the list of it’s params:

• $blog_id
  (int) (optional) Blog ID of the created blog.
• $user_id
  (int) (required) User ID of the user creating the blog.
• $domain
  (string) (optional) Domain used for the new blog.
• $path
  (string) (optional) Path to the new blog.
• $site_id
  (int) (optional) Site ID. Only relevant on multi-network installs.
• $meta
  (array) (optional) Meta data. Used to set initial site options.

So in your case you can use it like so:

function add_users_to_new_blog( $blog_id, $user_id, $domain, $path, $site_id, $meta ) {
    // get users you want to add to new blog
    $users_to_add = new WP_User_Query( array( 'blog_id' => 1 ) );  // <-- change that 1 to proper blog id

    foreach ( $users_to_add->get_results() as $user ) {
        add_user_to_blog( $blog_id, $user->ID, 'administrator' );  // <-- change administrator to any role you need
    }
}
add_action( 'wpmu_new_blog', 'add_users_to_new_blog', 10, 6 );