Snippet to change the default WooCommerce shipping method. Supports PluginHive Shipping Plugins: https://www.pluginhive.com/product-category/woocommerce-plugin/woocommerce-shipping/

functions.php

function wf_default_shipping_method( $method ) {
        $the_cheapest_cost = 1000000;
	$packages = WC()->shipping()->get_packages()[0]['rates'];

	foreach ( array_keys( $packages ) as $key ) {
        if ( ( $packages[$key]->cost > 0 ) && ( $packages[$key]->cost < $the_cheapest_cost ) ) {
            $the_cheapest_cost = $packages[$key]->cost;
            $method_id = $packages[$key]->id;
        }
	}

	return $method_id;
}
add_filter( 'woocommerce_shipping_chosen_method', 'wf_default_shipping_method', 10 );