How to use PhpSpreadsheet without installation (like PHPExcel)
In your case there are two options for you!
Answer: 1
Alternative method without terminal
Run composer with a PHP script in browser
Answer: 2
Third party sites, which allow to download composer packages online. get PHPspreadsheet latest version.
https://php-download.com/package/phpoffice/phpspreadsheet
Bonus You can download almost any composer packages @ https://php-download.com
Have you considered installing composer locally, running it as instructed, and then just sending the generated files to the server via normal FTP? You install composer on your computer and run it there, then upload via FTP/SFP...
Composer is not "necessarily" intended to run live while the user is downloading the pages, it is intended to be run "mainly" on your local computer and generating the files and dependencies that later on you upload to the server. It can update the files on your server, but that is a convenience not a necessity.
By registering custom autoloader and PSR simplecache autoloader it is possible to fully workaround composer installation - see:
https://github.com/PHPOffice/PhpSpreadsheet/issues/31#issuecomment-354502740
Please note, that installation via composer is currently the only officially supported solution.