I've experienced this same phenomenon as well. My hypothesis is that it's related to the matchmaking filters and rating ranges. In other words, let's say I fire up a FFA game where my rating is something like 1615 and my matchmaking filters are 1500-maximum. Then let's say the next player in the queue fits my criteria, but his filters are somehow incompatible with mine, such as maybe his rating is 1505 and his preferred range is 1400-1600. Or we find a third player who fits both of ours but has incompatible overlap somehow.
So maybe that's a messy explanation or maybe it's completely wrong, but I agree if you just cancel and retry then it resets your matchmaking and the game often ends up starting immediately
I thought it is just a coincidence. Now I am sure it is not:
1. You click [New Game] button and wait for long time. The server can not find opponents (and teammates) for you. You click [Cancel]. Then click [New Game] again and appear in a new game after 1 second. It happened many times. So, it can not be a coincidence. It is some error in the matchmaking system. So, if the game does not start in 1 minute, just Cancel and then New Game again! Do not waste your time waiting.
2. You click [New Game] button and wait for long time. The server can not find opponents (and teammates) for you. You click [Cancel] and ... a new game starts and you appear in that new game. It also happened many times. I can not prove this, but it does happen. Is it a bug? A feature? A coincidence?