It takes almost 4 minutes to start a game (Dota2) and another 3 to start a match after accepting a match. this always happens only on my first match. The subsequent matches load relatively quickly, but when i quit the game. My entire system is slowed down for some reason and it stays this way till I restart the computer. My computer configuration is enough to play the game at basic graphics.
I had the same problem when I installed steam. The game was DreadOut (I wouldn't recommend it) and it used to take a couple of minutes displaying a black screen before the game actually started.
What I have done is install the graphic card manager in order to optimize the gaming settings.
I don't know what graphic card you have but in my case it was an AMD and I have ubuntu 14.04 so I installed Catalyst control center using this video
Optimize my gaming settings and then the problem was over.
I hope this helps,