Try to activate the application (if it is open, of course), open the window menu and select Maximize. All this via sendKeys. It worked for me.
Set WshShell = WScript.CreateObject("WScript.Shell")
WshShell.AppActivate("Adobe Illustrator")
WshShell.SendKeys "% " ' Send Alt+Space
WScript.Sleep 100
WshShell.SendKeys "{UP}"
WScript.Sleep 100
WshShell.SendKeys "{UP}"
WScript.Sleep 100
WshShell.SendKeys "{ENTER}"