The gist of it is to use this method introduced in iOS 7:
https://developer.apple.com/documentation/uikit/uiscreen/1617814-snapshotview:
With that you get a UIView containing a screenshot that includes the status bar. Once you have that, it’s just a matter of hiding your current view then pushing the screenshot view around.
I posted a proof of concept here:
https://github.com/simonholroyd/StatusBarTest
NOTE I haven’t submitted code that does this through the Apple review process, but this is not a private API method.