I think generally you can place an order before the market opens, maybe even the day before, but that doesn't really give you any pricing power. It will still pop at the open and your order may not clear until it does. But that may still put you ahead of the Robinhood masses.
Better option might be to try a pre-IPO trading platform like EquityZen.
"Shares that are the subject of investment through EquityZen are generally subject to a lock-up period of up to 180 days after the effectiveness of a company's IPO filing, during which time shareholders are restricted from selling their shares."[1]
The 180day lock-up period could EquityZen poorly suited for investors with a short time horizon.
Could you do what Mark Cuban did and work with your brokerage to do sell calls & buy puts around the strike? That would lock in your price for a given amount of time.
If you had a sizable fortune at stake, you'd go to a major financial firm like Goldman Sachs, which handled the collar for Cuban, and they'll build you something custom. Almost any arrangement can be worked out, with a fat fee to go with it.
That only applies to IPOs. In a direct listing the shares start trading at the published reference price. There is no underwriting or other ceremony around it.
For a direct listing, does that mean Coinbase could conceivably charge any price they want for a market order given they are the only seller when it is first listed ?
Other existing shareholders can sell as well (there's no lockup), and I guess short sellers could sell immediately? But yeah issuing a market on open order for a new stock would be a "courageous" move (but IMO that's true of any market order - don't use a market order instead of a limit order unless you're genuinely willing to buy at $999 / sell at $0.01).
Better option might be to try a pre-IPO trading platform like EquityZen.