I'm not sure if there's a way to automatically check a download date.
But you can certainly set a date for when the app was very first launched. In your appDidFinishLaunching method in your app delegate:
if (![[NSUserDefaults standardDefaults] objectForKey:@"FirstLaunch"]) {
[[NSUserDefaults standardDefaults] setObject:[NSDate date] forKey:@"FirstLaunch"];
}
Any point after this, you can check this date and compare it to whatever you want.