A plausible next step to me is something like the Amazon Corner Store, where they have neighborhood caches of goods. I go to order something and they say, "Hey, we figured you might want that, so it's just down the street if you want to pick it up now, or we'll drop it off later today." Or once self-driving improves a little more, maybe a mobile truck-sized warehouse with delivery bots, so they get delivery times down to 10 minutes or so.
And for the future, they have huge historical baselines for a lot of customers; I've been using them for more than 20 years. Most of the day their software sits in my pocket, so it wouldn't be hard for them to start collecting the sort of sensor data that gives them a very good idea of my activities and metabolic stats. It seems entirely believable to me that they could know that, for example, colds are going around, that sensor data indicates I'm going to feel the symptoms soon, and to dispatch a delivery robot with a package of tissues, OJ, and Nyquil.
"Amazon has filed a patent for a shipping system designed to cut delivery times by predicting what buyers are going to buy before they buy it — and shipping products in their general direction, or even right to their door, before the sales click even (or ever) falls."
Realistically they were looking at items added to your cart but not yet purchased, and moving them to a closer distribution center in case you purchased.
Put another way, shit shows up in my mailbox for which I took zero action? Mine now.