In this approach you would run the existing installer (which doesn't have a silent mode - otherwise why are you doing this?) possibly using a tool like "AutoIT.EXE" to cause appropriate mouse and keyboard events to occur as if a user was actually operating the installation.
This approach needs to be very well tested and almost positively will fail if your MSI needs to be deployed silently (in which case you might want to use the "AbortIf" command to abort if someone tries to silently install it (or otherwise deploy it in a manner which prevents the keyboard and mouse automation).
The user can also try to use the keyboard and mouse while the automation is taking place so your script should be written as defensively as possible, for example by putting windows in focus and moving mouse immediately after without delays in between.
I would recommend a follow up custom action to validate the installation worked, and perhaps the error message could explain reasons why it could fail.