See the filtered search portals in this demo file: https://www.dropbox.com/s/0pm1gdqcfi2ndpv/EnhancedValueSelection.fp7
It's in the older file format so Filemaker 12 and newer users will need to use Open from FileMaker's File menu to open this file in order to produce a copy of the file converted to the newer file format.
The "starts with" search portal could be modified to do what you want. Each button could set the search field--which does not need to be present on the layout if you are only going to use the buttons, to a different letter of the alphabet. Each button can perform the same one line script but have different letters of the alphabet passed to the script as a script parameter.
Can I get the above demo file link again for filtered search portals being presently it is inactive.