Note that Prime Now, Amazon Fresh, and Amazon Pantry are all different services with different availabilities, and I can often find things on Prime Now that aren't on Fresh (haven't even tried with Pantry). Delivery slots haven't been abundant but can typically be found within 2-3 days.
Seattle-area groceries are mixed - some doing well at social distancing (have 6-foot spacers marked for a line outside, and letting in limited shoppers, with more going in only after some come out), some not so much, especially at peak times. Early morning (before 7) or late morning (after opening rush, before 11) seem quietest. Employees and shoppers about 30% likely to wipe down basket and cart between uses, about 20% surgical mask usage, haven't seen a N95+ in a while. I feel pretty good with double-mask and nitrile gloves, and wiping down handles before use with a chlorine or alcohol wipe.
Driving is pretty safe, alone. It's probably worth going by a few different stores to find the one you're most comfortable with before going in. If you're walking or using public transport, your options are more limited.
The best plan for your food stockpile is to replenish and use it. Keep 3-5 weeks, shop when you're down to 3.5, buying up to 5.
Amazon Fresh doesn't deliver to my address, but with Amazon Prime, Amazon pantry, and Walmart.com I can still get a lot of food delivered to my door. I put packages in my basement (without touching them) and keep them there for at least 3 days before opening. If you don't have a basement, I suggest you put packages into a large garbage bag and leave them untouched for at least 3 days.
I live in a hot region, and have a car parked outside. I've been putting non-heat-sensitive packages in there for a day, since interior temperatures should be going above 130F / 55C, and easily killing any viruses.
I am going to 24 hour grocery stores in the middle of the night once every 2 weeks to reup to 6 weeks worth of food. I imagine this sort of thing is harder for people in denser areas.
Most or all the 24-hour grocery stores here (bay area) have converted to having closing hours, as far as I know, to help them deal with the logistical problems caused by overwhelming demand. You might expect this to happen in your area too, at some point.
I live in Boston. From what I am hearing, grocery stores are mobbed, day after day, and don't seem to be taking social distancing seriously. Is this a serious enough problem to keep R0 above 1, and prevent successful suppression?
I have about a 4-week supply of food but I want to save it for the worst 4 weeks of the pandemic. I will take my chances with delivery/the local convenience store until then, both of which involve lower exposure risk than the grocery store by 1-2 orders of magnitude. According to some projections, the worst 4 weeks are about to start. But that seems extremely optimistic to me. My naive expectation was that without social distancing the peak would be in June. Distancing should reduce how bad the peak is, but also extend it, assuming distancing is not sufficient to lower R0 below 1.
I can extend the life of the stockpile if Amazon Fresh ever becomes operational again. This involves non-zero risk, but one delivery a month from them is much less risky than daily uber eats/convenience store runs.
In an extended-peak scenario it doesn't really matter when I eat the stockpile because I am going to have to get at least some deliveries during the peak. But in a high and short peak scenario, both my ability to avoid all deliveries and the desirability of doing so are a lot higher. In a low and short peak (i.e. successful suppression), the desirability of avoiding all deliveries is less, but I maintain the ability to do so and I might as well, if I can predict it correctly.