You need to use an estimated date. Without an actual date, the program doesn't know if it's a short term or long term gain.
You really don't need the actual date acquired down to the day as the real distinction when reporting a sale is whether the holding is "long term" or "short term". If you know at least that than any day over a year before the sale (long term) or less than a year before the sale (short term) works.
If you can't come up with an reasonable estimate for the basis - one you think you could defend with the IRS if they ever asked - you pretty much have to go with $0 there.