So far I've learnt that phonegap doesn't have that way to get the installation date/time. You'll need to write platform dependent code and find a way to call them. You can also write a plugin to communicate between native and cordova.
In android you can get the installation time. LINK
PackageManager pm = context.getPackageManager();
ApplicationInfo appInfo = pm.getApplicationInfo("app.package.name", 0);
String appFile = appInfo.sourceDir;
long installed = new File(appFile).lastModified(); //Epoch Time
In ios you can get the FIRST LAUNCH date
In application didFinishLaunchingWithOptions
NSDate *date =[[NSUserDefaults standardUserDefaults]objectForKey:@"FirstLaunchTime"];
if (date == nil) {
// nil means your application running for the first time
[[NSUserDefaults standardUserDefaults]setObject:[NSDate date] forKey:@"FirstLaunchTime"]; // set the current time
}
And you can use them to uniquely identify the preference file.