Hi Marc,
There is no option for that unfortunately, we are not currently planning to add it either. Usually I recommend a custom code if possible, but there is no hook at the script location to add a bypass solution to this. The only way is to change the core files.
The autocomplete handler function is located in the wp-content\plugins\ajax-search-pro\js\nomin\jquery.ajaxsearchpro.js file, on lines 2320-2351.
You could add something like this:
if ( $this.n.text.val().length < 3 ) return;
..before this line (2334):
var data = {
The javascript loading method has to be changed to Non minified for changes to populate, otherwise the minified file is loaded.