Ok so I got to level 25, nothing out of the ordinary with my latest playthrough. Have just gone into Geirmund's Hall to get the final circlet for Forbidden Legend. I go to the chest which is near the entrance which has at least one fire trap in front of it. My most powerful weapon up to this point is the Ebony Warhammer enchanted with Fiery Soul Trap. (Not including spells or shouts and not upgraded as I still have a way to go before I can get the Arcane perk).

So I open the chest expecting maybe a bit of gold, maybe some arrows, maybe a soul gem, the usual minor stuff for this level. But was speechless when I saw there was a Daedric Warhammer in there. At level 25! I'd read that Daedric weapons weren't supposed to appear until level 46/47. I've never heard of this happening before (unless it's by using mods or something, and I'm on Xbox 360 so I can't). The earliest Daedric weapon I'd had in a playthrough was a Daedric Dagger which I got at level 37. This is for me the most awesome moment since I bought the game.

Has this happened (genuinely) to any of you? How rare is this?

Yes ! But instead I found some Daedric gauntlets early on which made for an awesome role play opportunity, once equipping the gauntlets I left them on as a sort of cursed armour which cannot be removed. A nice character defining find

Daedric Cuirass of Peerless Conjuration at level 18, but I was using the Atronach Forge in the Midden of the College of Winterhold. My character was (is) a Necromancer and the Enchantment actually fit the character.

Daedric Gear in the twenties is not common, but I have had it happen on a few characters. Often the Game gets Evil with powerful items found as loot, like a Warhammer for a sneaky archer that uses Daggers for up close.

My last assassin found a Daedric dagger at level 27. You can imagine my joy being that this character makes 95% of her kills by sneaking and slitting throats.

Pretty sure it's just a higher chance as your level increases. That's some serious luck! Gratz!

Yeah, it's quite rare but not impossible to find daedric gear while level is still that low. Requires just a bit of a luck.