Is it really that uncommon for someone like me to thoroughly enjoy Dominion but abhor MtG?
(Why: I don't see how it can be fun losing a game before your 2nd turn.)
Well that's why the cards that let you win on your second/third turn are banned in most formats.
Legacy has quite a few decks that can win on second turn with monster hands, Modern has a few too. I don't follow vintage.
But yeah, really, it is very rare for that to happen, and in Standard, which is, I believe, the most popular format, you do not win before turn 5 unless you open with god hand.
Upgrade - Birthing Pod (I love this one
)
Minion - Time Spiral
Chancellor - Reminisce
Oasis - Any looting effect, like Faithless Looting
Envoy - Fact or Fiction
Throne Room - Reverberate
Wandering Minster - Augur of Bolas (or scry 3)
Steward - any Charm
Moat - Counterspell
Rats - Relentless Rats (mostly cuz of numbers and flavor)
Scout - Chimney Imp
Black Market - Booster Tutor