It looks to me like this expression originated in the League of Legends community (which is still the gaming community that uses it the most, it seems). All of these are in reference to rating, which at the time was the Elo rating system.
So far I found something as far back as late 2015 via Twitter:
we are same pisselo only difference is u have 2k games HARD stuck next time u shower i hope it come gas — November 18th, 2015
Examples are much more plentiful starting in 2016, as this Twitter search shows. Late 2016 is also when I first found an example of it being written as one word:
faker hardstuck in D2 for 2 seasons Lmao —November 7th, 2016
Here are some more early-ish examples from across the web:
@Joekerism getting therapy for hard stuck d1 — April 1st, 2016
ok i admit it....im hard stuck in silver 3.....halp — April 14th, 2016
i had fun making some threads when pro players got placed like in silver at the beginning of the season and were hard stuck there until riot dished out the "fix" or they duo'd heavily and basically stomped games without mercy — December 17th, 2016
Yeah i'm currently so hard stuck in plat it's unbelievable. January 1st, 2017
personally i was hard stuck in d3 60 points exactly — February 6th, 2017
No offense, but LB is probably a bit too hard for you if you are hard stuck bronze. — February 6th, 2017
don't really care hey, at least im not hardstuck diamond XD — March 6th, 2017
Define hardstuck — April 4th, 2017