If you want to perform a silent install of ArcGIS desktop for Windows, you need to use the Microsoft Installer (.msi) file. You can follow the “Installing ArcGIS Desktop silently” guide from ESRI to get all of your parameters figured out. But finding the .msi file is difficult. The guide mentioned above doesn’t tell you where to get the installer and it’s nowhere to be found on the ESRI download site (that I could find).
It turns out to be quite easy to get the installer. First, download the ArcGIS desktop installation executable from the my.esri.com site. This will be named something like ArcGIS_desktop_108_172737.exe. Using Winzip, 7-zip, or another compression utility, extract the files just like you would with a .zip file. In the extracted directory, click into Desktop, then into SetupFiles. The desktop.msi file will be sitting right there.