If you want to perform a silent install of ArcGIS desktop for Windows using the Microsoft Installer (.msi) file, you need the actual .msi file. But finding the .msi file can seem difficult. 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.