Most likely only by editing the corresponding theme part of the site (or by creating a child theme). Unfortunately each theme uses different ways of displaying the default search form, so there is no universal solution.
The search form used by your theme is usually in the searchform.php or search.php file in the theme directory. Try to place the php shortcode for the ajax search pro if you find the correct file.
Best, Ernest Marcinko If you like my products, don't forget to rate them on codecanyon :)