For stock sales you will need something for an acquisition date, even if it is multiple dates. What it wants to determine is the holding period, which sets either a long-term or short-term gain or loss. Could you try "various" as is used in other contexts, assuming all those purchase dates are either long-term or short-term before your sale date?
As a workaround I think if I had to enter just one date and all of these shares were long-term, I might enter the newest acquisition date (closest to the long-short boundary). If it were short term, then I might enter the oldest of the dates.
Another way might be to import this data. If you had multiple lots of stock acquired on different dates it might generate all the individual purchases on separate Form 8949 lines -- much easier than having to enter every lot by hand with its own purchase date.
I hope this helps!
