I can come quite close to beating this without prizes, but I'm not sure how to work things mechanically. Throwing this up in case someone sees a way to set this up (I'm already assuming perfect shuffle luck):
Xroads (3 actions left) ->
Workshop (gain a tunnel) ->
Hamlet (draw a tunnel, discard a tunnel for action, gain a gold, 3 actions left) ->
Duchess (discard a tunnel, +2 coin, gain a gold)
Moat (draw two gold)
Buy province
A new luckless solution using a prize.
Xroads
Princess (golds cost 4, province costs 6, 14 total coin required)
Trade route copper (great hall, fairground, nobles, island, silk road, garden, estate, duchy, province, colony already having been bought means that you gain 10 coin)
Fools gold
Fools gold
A highly contrived solution, but no prizes:
Your opponent is running a black market deck and has bought a copy of every VP card in the game this means you can play trade route for 15 coin.
Play:
Hamlet (draw a copper from the discard, discard it for +buy)
Trade route (trash a copper, +15 coin, +buy)
3 FG (9 gold)
You now have 24 coin and can purchase 2 golds, a province, and something costing 4 coin.