We already do and have been doing that with selective breeding since at least 10kya. If you look at Norman Borlaug's shuttle breeding program, it moved really quickly and in a way there was nothing natural about it.
Selective breeding is far from playing God, quite the apples to oranges comparison; you're not altering the code, you're putting two different naturally evolved genetic codes together and if the pregnancy is successful then it naturally occurred and fits within the existing natural framework of evolution.