It does not contain information. It contains chemicals, proteins, etc. The genome is made up of molecules which are simply behaving according to the laws of nature. Information requires an abstract layer (the mind). We can get information from it (like we can from virtually anything), but it is not information from some designer. Just a chain of replicating molecules, like the game of life from John Conway.
Rearange the order and you don't end up with the same result, generally, it effects the organism in a negative mannor.
you answer your own doubts enigma,if that happened it would have to be the work of a god/gods, it's the only way a god/god's could prove they exist, and then we would still question it.
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