##Seriously, 43 bytes

6╙¬▀'_+,;)-@s`;0@Eùk`M┬i;╗;lrZ`i@╜í=`M@░' j

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The lack of regex capabilities made this much more difficult than it needed to be.

Explanation:

6╙¬▀'_+,;)-@s`;0@Eùk`M┬i;╗;lrZ`i@╜í=`M@░' j
6╙¬▀                                         push digits in base 62 (uppercase and lowercase letters and numbers)
    '_+                                      prepend underscore
       ,;)                                   push two copies of input, move one to bottom of stack
          -                                  get all characters in input that are not letters, numbers, or underscores
           @s                                split input on all occurrences of non-word characters
             `;0@Eùk`M                       for each word: push the first letter (lowercased)
                      ┬i                     transpose and flatten (TOS is list of first letters, then list of words)
                        ;╗                   push a copy of the first letters list to register 0
                          ;lrZ               zip the list of first letters with their positions in the list
                              `i@╜í=`M       for each first letter: push 1 if that is the first time the letter has been encountered (first index of the letter matches its own index) else 0
                                      @░     filter words (take words where corresponding element in the previous list is truthy)
                                        ' j  join on spaces