There is not a Trello board creation date available, however you can query the actions for the card and board and filter on createCard or createBoard actions, but you're limited to the most recent 1000 actions using the API, which can be a problem for larger boards.
This article below will explain the steps which may give you a close estimate of the creation date by the date the first card was created, as long as you didn't have more than 1000 transactions in that board.
I hope this helps!
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