Something's wrong here. They should not be asking you for that information. If they don't have it, they should be reporting cost basis undetermined. You of course are ultimately responsible for reporting the right cost basis and the right dates, not them. Bummer! It sounds like a lot of work is ahead.
In some cases when, despite your best efforts, cost bases are not recoverable, the best you can do is come up with an appropriate approximation.
For instance, Bob TT transferred his account for one brokerage to another, and then to another, and somewhere along the way the cost basis was lost. Then this year, Bob TT sold his investment. Unfortunately he didn't keep records of his purchases because he assumed the broker was tracking it--or they got eaten by the dog, whatever. So now Bob TT figures he originally bought the stock (crypto in your case) in 2000, probably about May, so let's say May 15, and he looks up in the historic tables and finds the closing value on May 14 was $10 and on May 15 was $11 per share. He uses $10.50 per share for the 100 shares plus $105 in transaction costs, which is about what his broker was charging back in May 2000, and reports the basis for the 100 shares at 1050+105=$1155 on May 15, 2000. Since the sales price on June 13, 2023 was $11100 for 100 shares, he reports a LT gain of $11100-$1155 and lists this with Box E checked, because he got a 1099 but it didn't list the basis.
