The reason you might not be able to view the plugins menu in WordPress is if your site is part of a WordPress multi-site network and the network admin has disabled the plugins menu item for network sites.
You might contact your network administrator to install plugins for you to address this problem.
In my case, the button was missing because it was a multisite install. The Add New button appears only when you go to top bar -> My Sites -> Network Admin -> Themes. From there, you can add new themes and enable them for the rest of the network.