Since it has essentially the marketplace problem (two separate audiences, neither of which has any incentive to participate without the other), you can use the classic marketplace solution. Assert the existence of one side of the marketplace. Work like a dog on acquiring the second. Use your possession of the second to bring the first on a bit more legitimately.
They're not selling anything which doesn't already exist, in readily accessible quantity, in their target markets. Thus, handwaving away the problem of lacking supplier relationships is easy. You just go to them like a normal consumer, pull stuff off the shelf, and pay with your credit card. Then you pack it personally or with a team of underemployed people, and deliver it in a similar fashion.
This "doesn't scale" but carries little execution risk, and lets you focus on the (first) really hard problem, which is "How do I sell $100k of groceries every single day?" After you're selling $100k of groceries every single day, doors open magically. Those particular doors don't help you bring on more customers, though, so don't focus on opening them prior to having customers.