Do you mean pub dungeon or instance dungeons?

For pub dungeons, they are everywhere, and most already have people in them, so you can clear it out relatively easily/already cleared out for you and every1 is camping at boss.

For instance dungeon, the first one is the banished cells, fungal cavern(?) and spindle clutch, they are around 12-15 and you do them in groups of 4. Instance dungeon only have you and your group in them and they give you skill point and rewards only for the first time you complete it, second times and so on, gives you only loot from chests and mobs.

There are two ways to do four man instance dungeons, have 1 tank 1-2 healers and 1-2 dps. And like i said, you need four people to do it, sure you can solo them, but you have to be very high level in contrast to the dungeon you are going into, such as lv 30-40 for the banished cell if you go solo. That or you can do it as a low level with a couple of higher level players, like yourself at lv 7, 2 at around 16+ with 1 lv 20, though you would still need a healer.

But generally the first pub dungeon opens up almost immediately, you just have to find em. The instance dungeon you have(More along the line of recommended) to be lv 11 minimum and a specific class to be considered an invite into a group.