After living in caves (IF you believe that's accurate), what was the first type of above-ground dwelling that humans constructed? ~

Probably some kind of lean to made of leafs pulled together. 

WHAT DO YOU MEAN IF I BELIEVE THAT IS ACCURATE?

YOU DON'T BELIEVE PEOPLE LIVED IN CAVES NOW?  ARE YOU KIDDING ME? ?????

"lean-to" or "tee-pee" type dwellings, I imagine.

People still live in caves in Afghanistan and, I'm sure, other places in the third world.

Ice-age humans constructed tents.  At least 8000 BC people were making bricks to build structures.

This was interesting to read.  https://www.localhistories.org/houses.html

Caves suitable for habitation or other human use occur only in particular regions, and then are in something of a minority of that area's caves, so although definitely used, many prehistoric people must have had to make some other form of shelters. 

The first such probably were something like My2cents suggests, made from leafy branches and perhaps animal-skins.

They lived in huts until the Golgafrinchans arrived.