Windows Search has improved steadily through the years, especially now with Windows 10's smarter Cortana enabled search bar. So far, it does a fine job executing computer commands, opening programs, and completing basic searches locally or on the web.
File Explorer's search bar, though, is another story. It remains slow and clunky, with limited granular controls on the surface. For quick and advanced searching, a third-party solution may just be the ticket.
A solution like Binary Fortress' FileSeek. FileSeek is described as a "lightning fast, small and easy to use" search tool for Windows and boy, is it fast!
For comparison, I ran a general search for ".txt" files on my C:\ drive with Windows 10's standard Explorer search bar and it took about one minute and 16 seconds for it to complete. Running the same search for ".txt" files in FileSeek, however, took only about 10 seconds.
These blistering search speeds are possible because FileSeek uses a more efficient multithreaded search process and there is no background indexing involved. Without background indexing, FileSeek is easier on computer resources and it won't bog your system down.
Its interface is a bit more complex than the standard Window's search bar but once you get the hang of it, you'll be searching for files in no time.
You have your straightforward "Path" and "Exclude Path(s)" boxes for browsing your search locations (including network shares) and the "Include Files" and "Exclude Files" for your search terms and parameters.