Skip posts, but keep posts per page

Use pre_get_posts to add a meta query to the main query:

function wpd_date_meta_query( $query ) {
    if( $query->is_post_type_archive( 'your_post_type' ) && $query->is_main_query() ){
        $meta_query = array(
            array(
                'key' => 'Date',
                'value' => date('Ymd'),
                'compare' => '>=',
                'type' => 'NUMERIC'
            )
        );
        $query->set( 'meta_query', $meta_query );
        $query->set( 'meta_key', 'Date' );
        $query->set( 'orderby', 'meta_value_num' );
        $query->set( 'order', 'ASC' );
    }
}
add_action( 'pre_get_posts', 'wpd_date_meta_query' );

Also note that while your current date format may appear to function correctly, you will get unexpected results with any format other than yyyy-mm-dd, because it is simply an 8-digit numeric comparison. Alter just the year and you will see how the current format fails.