The fastest strategy right now is just to do as little as possible, since you start with a $600 lead as a Flapper. You just rely on event RNG to limit the AI's mule profitability and gambling RNG to deliver a victory.

But knowing some mechanics can both make you slightly faster and slightly more likely to win.

Clearing messages: No mashing is required. Both A and B buttons count as "The Button" (thanks Atari) and either one works. You hold a button to clear on the first possible frame, but you must alternate which button you hold each time. If there's an opportunity for valid inputs where you press neither button, for example during the auction timer, both become hold-to-clear options again. The messages that require clearing are: before each player takes their turns, the end of turn event, the "surplus" message that appears after production of food/energy, and the score screen.

Food: In general, keeping the store empty after a fire is key to speed. But food in particular has a benefit if you have some. For each food up to the round requirement, you have more turn time, and each food's worth of extra turn time increases the gambling max by $50ish. Buying up to the required food at $15 returns $10 expected profit. Block river tiles from AI, these produce 4 food instead of 2.

Smithore: Always worth $50, never worth buying from opponents, as the worst case is a pirate ship steals your smithore inventory. The store never keeps smithore to sell, so if no one produces any, the auction is always fully skipped. Smithore production is impacted by how many mountains are on a map tile (+1-3), so when claiming tiles, pick the ones with the most mountain images to block the AI.

Energy: You don't use energy, so buying it adds no value to you. But keeping the store empty is an important speed strategy, so you will buy it at times. It spoils at 25% rounded down, which means you lose little money if you are buying at $10. All tiles produce energy, so blocking strategies matter less. Plains 3, river 2, mountains 1.

A note about market prices and how it can give the AI a big lead: The "market price" starts at the minimum for food and energy. AI will adjust its production if market prices change, and at times will abandon late-game smithore production if another good is more valuable. The price of something will rise if the combined inventory of all players+store is less than the required amount for next round. This happens often for food after a store fire, since you require as much food as the AI just for existing, and produce none. This is less common for energy as its dependent on how many mules are put to work, and also excess energy spoils slower. If you aggressively claim river tiles, you (intentionally) decrease food production and increase the odds this happens, so it helps to understand this mechanic.