Publication within copyright law can be a complicated concept. As a general rule, in order for a work to be considered published, the copyright owner must authorize the publication and make multiple copies of the work available to the public.
A small publisher inquired whether the publication date would be “the date your books emerge from the bindery, the date the shipment arrives at your warehouse, the date you send out review copies, or the date you sell your first copies. I would argue that for copyright law purposes, the date you offer the first copies for sale is the date of publication.