Relatively widespread use of 'gymtimidation' in the popular press, as represented by the corpus at newspapers.com, appears to have started 01 Apr 2013 (paywalled link) with an ad for Planet Fitness in Poughkeepsie Journal (Poughkeepsie, New York)
01 Apr 2013, p A1, col 4:
NO NO
GYMTIMIDATION LUNKS

The caveat is that the newspaper corpus I used to determine the extent of use is not comprehensive, although it is large. Searches in other relevant corpora at English-Corpora.org did not produce earlier use of 'gymtimidation'.
However, the earliest use of forms of the term in the popular press was in the (paywalled) Elko Daily Free Press (Elko, Nevada) of 23 Jul 2002, p 15 col 1:
All those who are gym-timidated need, says Dart, is a little guidance.
The appearances in the popular press suggest that the word was in widespread spoken use among gym users and operators before it appeared in print.