There isn't a way for me to run composer on my server for a bunch of reasons. Is there any way to include all the files necessary to use the library?
@Lubosdz answered the question in the right way here:
How to use PhpSpreadsheet without installation (like PHPExcel)
Just coping files isn't enaugh to get it worked because composer is used to autoload all PhpSpreadSheet classes.
Without composer, you have to create your custom ones.
You can find a 4 steps method, files, and code here:
https://github.com/PHPOffice/PhpSpreadsheet/issues/31#issuecomment-354502740