We have never actually been given any indication that teh birth of a titan is damaging to the planet beyond an offhand mention somewhere of the titan looking like the surface of the planet close up.
Given how small teh world soul is, and how the titans seem perfectly able to take ethereal form before forming fully, i would expect that the birth of a titan probably jsut entials the world soul drifting out of the crust and forming in space, if Argus could be taken from Antorus to teh seat of the Pantheon, i don't see why a titan can't do the same to itself.