Here's my prior post on another thread. Hope it helps.
Saw my delivery button today as well. I'm not sure exactly when it first appeared since there was no related email. Tesla should fix this lack of notification, since they've trained us all to look for emails, although I suspect its appearance was pretty recent. For those anticipating their "button", from my experience (East Coast P85) it looks like it's under two weeks from signed paperwork to the delivery button, and 4-6 weeks from that to delivery (my window is January 30th-February 13th).