Is it possible to get bed bugs from food delivery?

Hey all, I'm beginning to have suspicions that I may have bed bugs. Haven't seen any as of yet, nor have I seen the usual clues (shells, stains, droppings etc.), I just have bite marks to go off from. The thing is, all of this happened while I was recovering from a flu. I hadn't left my apartment for over a week, but I did order food quite a lot. So my hunch is that one of the delivery person had bed bugs, either in their car or in their thermal bag, and it latched onto the bag. But now I'm wondering, is this even possible?