I struggle with a similar problem - I use a weekly food delivery service that delivers in a rather large polystyrene box and two ice packs. They offer to take last weeks when they deliver to recycle them, but leaving it out is rather difficult to do in my large apartment complex so I have to resort to always leaving them in the garbage room and I feel terrible for not recycling.
Depends. A single delivery truck running a route for 20 customers is a heck of a lot more environmentally friendly than those 20 customers driving a car each to the store to load up.
It's more environmentally friendly to not drive. In Netherlands it's common to have a supermarket very close to your home (walking distance). Else you use a bike. A car is when you have a family and then you'd stock up for a week of supplies.
We started using Amazon Fresh a few months ago, and they deliver in reusable totes. You collapse 3-4 of them and stick them in an in-collapsed one and leave it out for pickup the next time you have an order. Really wish the rest of my amazon stuff would come this way.
Youfoodz (horrific name, great service) actually. Delivers whole fresh meals rather than raw ingredients http://youfoodz.com
I've used HelloFresh in Australia, a competitor/alternative to Blue Apron and the polystryene box they use is much much smaller because it only contains the small meat items. The Youfoodz box is much bigger https://cdn.shopify.com/s/files/1/0506/7861/files/Blog-Zarah...
HelloFresh (AU) recently switched [0][1]: they now use WoolCool (compostable & recyclable), plus gel ice packs (cut open and dispose of gel, recycle packet). Also means you don't need to return the boxes, which is handy in an apartment building.