Think about what else you have warm in the house? Can you use any of your Winter attire? How about some towels? Any one of those items can also be used for a pillow if you need them.

Not having a go here, but I'm genuinely curious what you were using for a pillow and blankets before you moved. Surely you owned something!

if you're cold enough, sleep under your winter jacket. I've done that before when times were tough. In my last move, I was the opposite. my air bed wouldn't stay inflated through the night, so I slept on the floor with a blanket & pillow for a few months until I could buy a mattress. At least you have a mattress. Cover with a jacket and use something else as a pillow if need be.

Towels and sweaters

LMAO this happened to me this year too, except I was in my third trimester of pregnancy, and it was my air mattress that the mail man decided not to deliver and to send to my previously listed address (which is in another state and I haven't lived in for 5 years) because the house looked "empty". NO SHIT BITCH WE JUST BOUGHT IT. Idk why he thought creeping through our windows was acceptable either.

You own absolutely no bedding or blankets of any kind? That seems odd.