In my experience, it is not uncommon for a delayed departure time to be announced and then the flight leaves significantly earlier than that time.

For example, at 7pm the airline may announce, "We're waiting on crew from another flight who are scheduled to arrive at 8pm, so the flight will not depart until 8:15 pm."

A few minutes later (at 7:05 p.m.), "We found a different crew and we'll be ready to board in 15 minutes."