Why doesn't global $wp_query not get hooked?

I have a plugin that helps me to make lazy loading on posts of a custom post type. The idea is to add an action to the template_redirect/init and get data from the global $wp_query to make jquery understand how much loading there needs to be done.
The plugin php file looks like this:

function pbd_alp_init() {
   global $wp_query;

   // Add code to index pages.
   if( !is_singular() ) {   // can i select a specific post type here?
      wp_enqueue_script(
        'pbd-alp-load-posts',
        plugins_url( 'js/load-posts.js', __FILE__ ),
        array('jquery'),
        '1.0',
        true
      );

      // What page are we on? And what is the pages limit?
      $max = $wp_query-max_num_pages; // this returns 0
      $paged = ( get_query_var('paged')  1 ) ? get_query_var('paged') : 1;

      // Add some parameters for the JS.
      wp_localize_script(
        'pbd-alp-load-posts',
        'pbd_alp',
        array(
            'startPage' = $paged,
            'maxPages' = $max,
            'nextLink' = next_posts($max, false)
        )
      );
  }
}
add_action('init', 'pbd_alp_init');

Im sure that max_num_pages function returns a number when i call it directly - why does my global $wp_query seem to be empty?
In the documentation it says that the action should hook to the 'template_redirect' but 'init' seem to be more right? Both doesn't hook up to the wp_query..