The first one done in competition was in 1984. Two others did it in 1986 and then it was officially submitted to the code of points by another in 1987. It never really became a vault of note at this time because of its rarity and because it was not rewarded- hence the rarity. 1992 was the first time it 'made' it as vault, performed by Tatiana Lysenko. FTY's were still the vault of choice then and the DTY did not really begin to reign supreme until 2000, 16 years after it was invented.
Elena Gurova performed this vault at the age of ELEVEN in 1984. Elena was a member of the 1987 silver winning Soviet Team at the world championships, but pretty much fell through the cracks as far as individual stardom was concerned at a time when USSR was far deeper talent wise than America is now. Unfortunately, there is no video evidence of her doing a DTY. It is accepted that she did do it nevertheless, much like Stella Zakharova is credited as the originator of the double layout at a meet in 1977.
Aleftina Priakhina- innovator extraordinaire- and Elena Shevchenko are also given credit for performing the DTY first, in 1986, one year before Baitova actually brought it to a world championships and got it named after her. Certainly they were among the first, but both were two years after Gurova first did it. Here is Priakhina's.
Elena Shevchenko's, again in 1986.
Here's the one that took the naming crown, though unlike the amanar it's never called after her when used now. She was also extremely lucky as she performd it only a few minutes before Eugenia Golea of Romania, and a rotation or two before Yelena Shushunova.
And here's the one where the DTY actually captured attention, performed as it was among a whole host of much easier vaults, and then grossly underscored into the bargain. Tatiana Lyssenko, 1992.
And here we have one of the best ones being performed at the moment, 20 years after Lysenko's and 28 years after Gurova's. Kyla has the benefit of the vaulting table, better springboards and mats and yet Gurova's rivals it except for the more controlled landing. Fascinating what could be achieved back in the day.