Hello, welcome to phpBB.
I’m not aware of a way of automating the installation any more than it is already. If you haven’t got a board up and running an extension would be no good to you and a ‘script’ would still need uploading to the server so you wouldn’t be gaining much. If there is a way of doing it ‘automatically’ I’m sure someone will chime in.
The regular installation process, apart from having to upload the files using FTP, is pretty much automatic. You have to input some details but that’s normal for most types of installation. Learning to use FTP is well worth the effort as in the long run it will aid in your ability to maintain your website. In any case, if you use a desktop computer, you probably already know how to perform the standard copy/paste routine, FTP works in a similar fashion to MS Explorer apart from the connection to a web server.
There are many hosts that offer ‘one-click’ installs, which still need input but, be warned, these types of installations can cause issues. If you search here you will see many problems caused by such installs where the only way to fix them is to upload the files from here using FTP.
Also: Sites offering ‘one-click’ installers don’t support installation issues caused by the installer and generally send their users here for help.
Boards that have been created with a 'One Click' install provided by your host differ from boards installed with the files downloaded from here, and therefore we are unable to offer support. Softaculous Support can be found HERE
and Installatron Support can be found HERE