No, you enter the sold date as the acquisition date. When you sold the option to open (STO) you established the short position, or you acquired it. The premium you received at that time is your proceeds. When you buy to close (BTC) the position, you disposed of it. You would enter that as the date sold. The premium you pay to close a position is your cost. If you the short option expire worthless, your cost basis is zero.
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again the "expert" is not quite correct.
It is unfortunate that the broker's 1099-B does not correspond with the requirements of the IRS for short positions.
You are acquiring a security to close your short position.
That happens on the date you close the trade and that is Date Acquired.
The security purchased, an option, settles one business day later. That is the Date Disposed.
The day you entered into the short position is irrelevant.