Short answer: No, there is nothing stopping a player from confronting Dagoth Ur right from the start, but you will need Sunder and Keening to actually accomplish anything.
Ghostfence is fairly easy to get past. The gate is IIRC openable right from the start, you can levitate over the fence anyway, and if all else fails, the Scrolls of Icarian Flight can get you pretty much anywhere; just use a second scroll, or any source of Slowfall or to land, and you're done.
Without Sunder and Keening, though, you've no way to actually destroy the heart, so you'll need to go grab those on the way. Wraithguard can be safely skipped, as long as you have some way to survive the damage caused by the other two artifacts. That's not an easy thing to do, but it is certainly possible. A common method involves getting 100 pts of Resist Magicka, since the damage from Sunder/Keening is magical. The Heart Ring dropped by Dagoth in the first fight is handy here; even though it only lasts 30 seconds, that's more than enough time to destroy the Heart.
Ultimately, the game can be beaten without ever having to fight anything, or even complete any proper quests beyond the tutorial. But doing so involves running past some very strong enemies without the levels or equipment you normally need to survive them; look up Morrowind Speedruns on YouTube (or anywhere else on the internet speedruns can be found) to see some of the ways people survive the run into Red Mountain.