Even if you were able to enter solo at a high level I believe it automatically syncs you which would make it impossible. I am not positive on this aspect, but I'm relatively sure since I was synced to 20 as a lvl 23 entering the Copper Mines. Beyond this, (and again, this is if it were even possible to do so) you would not want to wait until you are so high above a dungeon that you could solo it. The story quests require these dungeons, and the story quests are important to get done as soon as you are able considering they give good exp, occasionally grant skills, occasionally have nice equipment as a reward, and unlock things like airship and choco travel. It's certainly not something you want to put off.

I enjoy playing solo as well, but using the Duty Finder and getting instance-matched is only a matter of clicking a button and waiting. The dungeons are not difficult, and at some point you will need to learn party dynamics or you will hit a brick wall in regards to progression.