Is it possible for it to be inpenetrable?
Yes, build it on a physical server.  Unplug the server and put the server in a time lock physical safe.  When the safe opens plug the server back in.

I can't imagine how it would be possible as a coded solution.  

You might be able to do something with an encrypted database, if you had some way to tie the encryption to a specific date.  Doing that would be a question for INFORMATION SECURITY

Related time-based encryption algorithm?