No way to install or add libraries?
Acquia has to have the full site, core, modules, themes, libraries, et.al. checked into their git repo in the format like:

git root
  docroot
    core
    modules
    themes
    etc.
    (includes index.php and other root files)


As Clive said, there is a pay for it CI process.  However, for the normal sites, you need to manage the site as a whole entity.  They do have Deployment hooks, but that is generally for clearing cache and the like.

FYI - I use composer on all my sites.  You run it locally and check in the composer files to the repo (e.g. the composer.lock, etc.).  Things like js libraries are added by manually adding repo's to the composer.json file if they are not composer friendly. E.g., here's how the jquery chosen plugin gets added:

"harvesthq.chosen": {
  "type" : "package",
  "package" : {
    "name" : "harvesthq/chosen",
    "version" : "1.8.7",
    "type" : "drupal-library",
    "dist" : {
      "url" : "https://github.com/harvesthq/chosen/releases/download/v1.8.7/chosen_v1.8.7.zip",
      "type" : "zip"
    },
    "require" : {
      "composer/installers" : "^1.2.0"
    }
  }
},


It's also best to have the Drupal friendly paths defined in your composer file.  E.g.:

"extra" : {
    "installer-paths" : {
        "docroot/core" : [
            "type:drupal-core"
        ],
        "docroot/libraries/{$name}" : [
            "type:drupal-library"
        ],
        "docroot/modules/contrib/{$name}" : [
            "type:drupal-module"
        ],
        "docroot/themes/contrib/{$name}" : [
            "type:drupal-theme"
        ]


These make sure things get placed properly by composer.