The tattoo didn't manifest until E.I.N. was awakened, which occurs when Z.W.E.I., or rather, the man who would become Z.W.E.I., is put to death by lynching by none other than Dumas. Possibly the original Dumas, not the Dumas that Nightmare assumes the identity of during SoulCalibur V. E.I.N. saves the man from death and forms a pact, and thus, Z.W.E.I. was born. This information is from New Legends of Project Soul, definitely worth a read if you have not already.
That being said, if you're saying that Grøh becomes E.I.N., not Z.W.E.I., then that would mean that he dies and becomes a werewolf spirit somehow? I dunno exactly how that would work. If he sacrifices his life and some weird Soul sword sorcery happens, perhaps, maybe, but worth noting is that Grøh'a insignia is that of a lion, and it has three swords, which contrasts the fact that he only has two swords. Z.W.E.I. gets a three-hilted sword from a blacksmith as some sort of bet (again New Legends of Project Soul), and maybe this could be the third sword.
I think we need to see Grøh's father before we draw any real concrete for sure conclusions. Grøh may be the man who becomes Z.W.E.I., and his father may be E.I.N., that is also a possibility.