Quick attempt:
Turn 1: Tunnel
Turn 2: Potion
Turn 3 (Draw 3xCopper, Tunnel, Estate): Tunnel
Turn 4 (Draw 4xCopper, Potion): Golem
Turn 5 (Draw 2xEstate, Golem, 2xCopper): Play Golem, gain 2 Golds, buy Herbalist.
Turn 6 (Draw Golem, 2xGold, 2xCopper):Play Golem, gain 2 Golds(4), buy King's Court
Turn 7 (Draw Golem, King's Court, 3xGold): Play KC/Golem, Gain 6 Golds(10) buy 2xTunnel
Turn 8 and 9 (Draw Golem, King's Court, 3x?) Play KC/Golem, Gain 12 Golds(22,30) buy nothing.
So, quick and unoptimized in 9 turns. I am thinking it should be easy to take a turn or two off of that. You can probably get down around 5 turns with something complex like the good old Puzzle 1 from the blog. (Since you can gain and play a ton of cards on turn 5, you can probably pick up the Tunnel/Golem/KC combo and play it all within the turn.)