Pagination not working in custom post type

As far I read in your comment, it isn’t requires for you to handle it with a custom query. So if you register your custom post type with 'has_archive' => true, then you can just reach the archive of the custom post type at http://www.yourwebsite.com/your-cpt-slug/.

Important: Remember to flush the rewrite rules after you change somethign related to your permalinks. You can do it just visiting Settings > Permalinks

See how register_post_type works for any doubt, it’s always lighting.