Get First File in Each Subdirectory Matching Extensions – Bash Guide

How do you get the first file in each subdirectory matching a list of file extensions? My goal is to run a program on just any one of the files in a series of subdirectories.

For example, below there are 3 subdirectories. I want to run the program on subdir1/file.dat, subdir2/file.d01 and subdir3/file1.dat given that I want to find files that have extension .dat or .d01.

subdir1 - file.dat, file.d01    
subdir2 - file.d01, file.d02, file.d03    
subdir3 - file1.dat, file2.dat

The following worked great for awhile, until I started to encounter directories like the last two. subdir3 is problematic, since all files end up getting processed.

find . -name "*.dat" -exec mixb {} \;