Lead with availability, not novelty
Customers respond to a clear answer to one question: can you bring it to me, and when. State the territory and the window plainly.
Use the channels you already own
In-store signage, receipts, your existing customer list and your online ordering flow reach the people most likely to try delivery first.
Do not promise what the operation cannot hold
The fastest way to damage a new delivery channel is to advertise a window you miss. Set a conservative promise and beat it.