Hi!
Yes, with a custom filter code it is actually possible. I believe you are looking for this tutorial: https://wp-dreams.com/knowledge-base/showing-the-category-titles-in-the-result-title/
To move the category titles before the actual title, just change this line from the tutorial code:
[php]$pageposts[$k]->title .= " ".$cats;[/php]
..to this:
[php]$pageposts[$k]->title = $cats .’ ‘. $pageposts[$k]->title;[/php]
I hope this helps!