Single word request: the person that "picks up things"

A person who drives vehicles is a "driver"

A person who swims in the water is a "swimmer"

What do you call a person who goes around and picks things up? "pickuper"?

It would be someone who literally grabs a box on the ground and puts it somewhere else (at higher altitude) ie: from the ground to a truck or from the ground to a shelve

An example:

A: I need to pick up these boxes
B: The pickuper will do it for you

What about picker-up? Similarly passer-by or hanger-on

https://www.ef.com/wwen/english-resources/english-grammar/compound-nouns/

loader

Dictionary.com:

noun 1. a person or thing that loads.

Example: "The truck loaders will be here in half an hour."

In the context of your sample sentence, collector would work. "The (box) collector" will do it for you. A "garbage collector" does exactly that.

Collector: "A person who collects things of a specified type." new Oxford American Dictionary.