You can hook into the rest api query and add your args from url’s parameters
The code will look something like:
function query_post_by_fields($args, $request) {
$url_params = $request->get_param;
//Modify $args with your url params
return $args;
}
add_filter('rest_post_query', 'query_post_by_fields', 10, 2);
Docs:
https://developer.wordpress.org/reference/hooks/rest_this-post_type_query/