Queues for max level 8v8 Solo seem to be under 5 minutes, often less than 2-3 minutes and sometimes within 1 minute. For the 4v4 group queue, our times have been as much as 20 or more--can be longer if you're only 2-3 people, since the game needs a full instance before launching.

Once the game opens, there's a ~1-minute lobby/prep time before it actually. There used to be a more common issue where you would successfully enter a game, and someone would reject the queue, and it would fail to fill, but these days my games have actually been filling within 3-4 minutes when that does happen. (If not, it empties out after 5 minutes and you just requeue, but I haven't had that happen lately.)