The commerce module has to be installed with Composer..The Commerceguys provide now an alternative. With Ludwig one can install Commerce without composer. The Ludwig module (Ludwig von Beethoven was a deaf composer --Drupal fun--) shows the manual way.
Install commerce module without composer and without activating..
Some other modules like address come with the commerce module.
After installation and activation of Ludwig, you will find with Reports => Packages an overview what to do. Download links of the libraries with the exact location for the manual uploads. Flush the cash and then the status becomes OK. Ready for your webshop..
I remind you that composer still has many advantages. An update with Composer updates the libraries. With Ludwig you need to do it manually. It is obvious that Ludwig has been made for them who don't want to work with Composer...Ludwig only works for the commerce modules.