Display Shipping Method based on the nearest Shipping Zone

I have an e-commerce site using Woocommerce WordPress. We have several branches that we added as shipping zones. I would like for the system to detect which branch is the closest and display the shipping method for that branch(shipping zone). I have figured out how to detect the nearest branch but the shipping methods displayed by WordPress is still based on the shipping address. So if my shipping address is in New York and I don't have any branch in New York, it will say that there's no available shipping method for that branch.

I've traced where the variable $available_methods is from and found it here. Is there a way to just provide the nearest branch and then the corresponding shipping methods will be displayed? I'm at a standstill on how WordPress/Woocommerce gets the rates. I appreciate any suggestions on this.

function wc_cart_totals_shipping_html() {
$packages = WC()->shipping()->get_packages();
$first    = true;

foreach ( $packages as $i => $package ) {
    $chosen_method = isset( WC()->session->chosen_shipping_methods[ $i ] ) ? WC()->session->chosen_shipping_methods[ $i ] : '';
    $product_names = array();

    if ( count( $packages ) > 1 ) {
        foreach ( $package['contents'] as $item_id => $values ) {
            $product_names[ $item_id ] = $values['data']->get_name() . ' ×' . $values['quantity'];
        }
        $product_names = apply_filters( 'woocommerce_shipping_package_details_array', $product_names, $package );
    }

    wc_get_template(
        'cart/cart-shipping.php',
        array(
            'package'                  => $package,
            'available_methods'        => $package['rates'],
            'show_package_details'     => count( $packages ) > 1,
            'show_shipping_calculator' => is_cart() && apply_filters( 'woocommerce_shipping_show_shipping_calculator', $first, $i, $package ),
            'package_details'          => implode( ', ', $product_names ),
            /* translators: %d: shipping package number */
            'package_name'             => apply_filters( 'woocommerce_shipping_package_name', ( ( $i + 1 ) > 1 ) ? sprintf( _x( 'Shipping %d', 'shipping packages', 'woocommerce' ), ( $i + 1 ) ) : _x( 'Shipping', 'shipping packages', 'woocommerce' ), $i, $package ),
            'index'                    => $i,
            'chosen_method'            => $chosen_method,
            'formatted_destination'    => WC()->countries->get_formatted_address( $package['destination'], ', ' ),
            'has_calculated_shipping'  => WC()->customer->has_calculated_shipping(),
        )
    );

    $first = false;
}

}