That would probably be the simplest solution. TryNinja, you could simply add an option to the search parameters to exclude all topic titles from the results that start with 'Re:'.
If you want the search to only bring the posts that titles doesn't contain "Re", you can do it yourself.
Just add
-Re to the post title field.
For example, in the image below I am searching for the posts that contain the word "bitcoin" and the title doesn't include Re.
Off course, it's not accurate to say every post that the title doesn't include "Re" is the first post of a thread. Users can edit the title and remove "Re" when making a reply.
This is an example of a search I was thinking about, but I made the mistake of putting a space after the '-' sign, so it didn't work the first time I tried it. Thanks for helping me to catch my blunder.
It seems to work now. @logfiles, I believe that's what you're looking for.
@TryNinja, ignore my previous comment. Maybe you should add an info icon next to "Post Title" to let people know that the advanced search works there as well.