Is there a way to automatically install the download?
The short answer is no, but in reality it’s not that hard to achieve it.
You can script the initial steps like unzipping (or pulling from git), setting permissions, installing PHP modules and options.
Then for the actual Install process there is a silent installer option, unfortunately it’s not very well documented or maintained. But it can be made to work. Search online for it.
Please share your findings if you make any progress. Thanks.