I've never used it but maybe something like TaskRabbit? Or maybe post to your local FB or NextDoor group looking for someone to help with "errands"? Maybe you can find a local person who would be willing to do the pick-up for a small fee.

Good luck!

I feel like you can postmate like anything, and I think I saw an app called grabit that might be worth looking into

I know you can't usually use 3rd party apps at places that don't have the restaurant portals, but postmates claims they can get you anything from anywhere. The thing is, it is complex, but this link kind of tells you how to do it. Basically though, you have to order from a nearby restaurant and then put in the special instructions what you've ordered from the actual restaurant you ordered from. Then, the driver will go to the general area, and then find the actual restaurant to pick up from. Pretty messy, so hopefully there are more options!
https://www.quora.com/How-do-I-place-a-custom-order-from-not-listed-place-restaurant-using-Postmates

Check the delivery apps themselves. Just because the restaurant doesn't partner with them doesn't mean the service doesn't go to the restaurant. I've worked in a few restaurants where the delivery service has done this.

I would recommend staying away from grubhub though. And keep in mind these services are also known to have higher prices than the actual restaurant, even when partnered with them.

As for which apps to use, I'm only familiar with the mainstream ones like Doordash and ubereats.

Depending on where you live taxi companies may pick up packages for a flat rate. They do groceries too. So as long as the restaurant will do a takeout order they should let a cab pick it up.

There may be more in California, but here in Texas there are DoorDash, favor, GrubHub, or Uber eats. I hope that helps

Order from some place that will deliver?