Sort by meta key on archive page

Use pre_get_posts to alter the main query before it is run. The action runs on every query, use the Conditional Tags to target specific queries.

function wpd_sort_by_meta( $query ) {
    if ( $query->is_home() && $query->is_main_query() ) {
        $query->set( 'meta_key', 'your_meta_key' );
        $query->set( 'orderby', 'meta_value_num' );
    }
}
add_action( 'pre_get_posts', 'wpd_sort_by_meta' );