The current turn 1 Empty the Supply that I'm aware of uses 2 events (Advance + Travelling Fair), so you can't do exactly the same thing. That said, we also get one free cost reduction with Allies in the game now, and new cards to work with, so maybe there's still a way.
You definitely need Villa or Cavalry so you can have multiple buy phases, probably both of them. And a way to get them back from the trash e.g. Lurker. Fortress also still probably good with Advance, though that locks out Travelling Fair. Sycophant or Guildmaster seem like the easiest Favor generators to feed Kingdom of Inventors. Maybe you can find a way to replace Travelling Fair with Galleria somehow?
So the usual turn 1 would be starting Necropolis, Cursed Gold, Pouch, Copper x2, and then you buy Fortress, Travelling Fair, Advance Necropolis into a Cursed Village getting War to trash the Fortress to put it into your hand, then Advance the Fortress into a Villa and go from there. So without Travelling Fair, you're really pinched for buys on turn 1.
I think you can probably do a turn 2 with that start though, without the final Advance because of buys. Start with Fortress + Cursed Village + Pouch + Cursed Gold + Copper, play out Pouch + Cursed Gold + Copper and you have $5 and 2 buys, plus a coin token. Buy the Galleria, Advance a Cavalry, play Cursed Village to draw 3 cards, then Advance 3 Cavalries to draw the Galleria and play it. And from there you can Advance Villa for net +1 Buy +$1 +1 Action, use the extra buys to Advance Gallerias, draw them with Cavalry, and play them for even more buys. Grab a Guildmaster for Favors and start reducing everything. Scepter + Lurker to gain Cavalries and Mandarins from the trash (topdecking your Scepters to play them again), and you can go infinite from there.