Make WordPress respond to a request for a URL that doesn't actually exist

virtual-page.php

<?php
/**
 * Make WordPress respond to a request for a URL that doesn't actually exist
 */

if ( ! function_exists( 'str_starts_with' ) ) {
	/**
	 * Polyfill for PHP 8's str_starts_with
	 *
	 * @link https://php.watch/versions/8.0/str_starts_with-str_ends_with
	 *
	 * @param string $haystack The string to search in.
	 * @param string $needle   The substring to search for in the haystack.
	 * @return boolean
	 */
	function str_starts_with( string $haystack, string $needle ): bool {
		return \strncmp( $haystack, $needle, \strlen( $needle ) ) === 0;
	}
}

if ( ! function_exists( 'str_contains' ) ) {
	/**
	 * Polyfill for PHP8's str_contains
	 *
	 * @link https://php.watch/versions/8.0/str_contains
	 *
	 * @param string $haystack The string to search in.
	 * @param string $needle   The substring to search for in the haystack.
	 * @return boolean
	 */
	function str_contains( string $haystack, string $needle ): bool {
		return '' === $needle || false !== strpos( $haystack, $needle );
	}
}

/**
 * Get the current URL of the request as detected by WordPress
 */
function helper_to_get_current_url() {
    global $wp;
    $current_url = home_url( add_query_arg( array(), $wp->request ) );
    $current_url = trailingslashit( $current_url );
    if ( ! empty( $_GET ) ) {
        $current_url = add_query_arg( $_GET, $current_url );
    }
    return $current_url;
}

add_action( 'template_redirect', 'action_template_redirect', 100 );
function action_template_redirect() {
    // If WordPress determines a page for this URL actually exists, then bail and show that page
    if ( ! is_404() ) {
        return;
    }

    $current_url = helper_to_get_current_url();
    if ( str_contains( $current_url, '/invite' ) ) {
        $redirect_url = '';
        // Do something to construct your redirect URL
        wp_redirect( $redirect_url, $status = 301 );
		die();
    }
}