Can I place a buy order during after hour session before the listing date of an IPO?

No, you cannot place an order for shares which are not yet listed in the stock exchange. Not even in the after-hours trading setting. But the exchanges allow a special pre-open trading session for IPO shares on a listing day (only first day of their trading). The pre-open session last for 45 minutes (9:00 AM to 9:45 AM) during which orders can be entered, modified and canceled. The listing price of the IPO share is determined between 9:45 AM to 10 AM by the exchange based on the demand and supply of shares came in the pre-open trading window. At 10 AM the IPO stocks actually start trading in public. If the listing price is equal or higher than the price you pre-open order to sell in pre-open; your shares are sold at the listing price in the pre-open trading session. If the listing price is lower than your sell order price in the pre-open market, your pre-open order will be canceled.