It seems only natural that, on everything but the most money-back boards, you would spend Cursed Gold to open with any general purpose trasher that trashes one or more cards per shuffle, for example Upgrade, Sentry, and Remake. Gaining the Curse slows down your thinning by one card, but so does not getting the trasher before the first reshuffle. Trashing two cards with Sentry or Remake before the second reshuffle already more than offsets the Curse. Consider that you have less starting Copper economy with Cursed Gold, so there is a higher chance that you won't be able to afford the trasher even before the second reshuffle (without spending Cursed Gold).
A similar principle applies when using Cursed Gold to open with a guaranteed junker. Opening Silver/Witch (with Cursed Gold)/Silver/Silver against an opening of Silver/Silver/Witch/Silver leaves both decks at about the same state by the second reshuffle, but the big difference is that the player who spend Cursed Gold to open Witch before the first reshuffle is guaranteed to have a Witch in their deck by the second reshuffle with only one curse in deck, whereas opening Silver/Silver leaves room to miss $5 without needing to spend Cursed Gold during the second shuffle, ending up with two curses by the end of the second reshuffle unless the other player had Witch drawn on Turn 5.
Trashers that only trash your treasure economy source like Pooka and Spice Merchant are a harder sell for using Cursed Gold in the opening. You have to be aware that you with be losing more and more of your economy each turn, and it's pretty slow to replace Copper with a Silver or a similar stop card that results in your deck not getting any thinner. Getting more cantrip +$1 while cycling is kinda cool, but trashing a Copper with say Pooka to get one of those is not going to increase your deck's total spending power, so you probably want to be trashing more than one card per shuffle or even turn or else getting a net increase in your total spending power.
Any card that does a good job of bootstrapping your deck's economy quickly, including through remodeling Cursed Gold, should be strongly considered for an opening Cursed Gold use, even if there is no Curse/Estate trashing (Pooka is always there for treasure trashing), because you are going to have a sucky economy for longer than usual if you don't spend the Cursed Gold that replaced a Copper. Artisan comes to mind as a good opening with Cursed Gold when the cards it gains are stackable.
Any card that provides both trashing and economy should be seriously considered to open with using Cursed Gold. Upgrade, Trading Post, Altar, Forge, and Remake all fit this bill.