At the moment, you need shell access and Composer on the server to install extensions.
One alternative is to run Composer locally and upload the files every time https://docs.flarum.org/composer#i-dont-have-ssh-access
Another alternative is our web-based package manager which is in beta. If you try the package manager you should still have a backup plan to be able to run Composer manually in case things go wrong (and you need Composer to install it in the first place). There's no complete documentation at this time, the extension to install is called flarum/package-manager and there is some documentation here https://docs.flarum.org/internal/package-manager
