It's not projecting to see the fatherly personality of MusukoGoji
No, even that is largely interpretive.
Godzilla displays paternal instincts to a degree, but he seems to be a lousy father.
He saves Minya twice sure enough, but in all other duties he's lax and lazy. Making him something of a Male African lion, with no females. Even then, he is generically protective. Even neglecting feeding Minya, to the degree a newborn must do it himself. This doesn't present Goji or Minya as very personified, but inversely makes them more animalistic, (Though admittedly, Minya has more personality than his father, in that it's a goofy little plaything) Godzilla acts like an animal protecting it's young, rather than any significant source of fatherly guidance. In fact, to the contrary rather than fatherly the movies climax makes him seem kinda neglectful. Minya is only captured by Kumonga as Godzilla was sleepy. Nothing says fatherly love, like letting your kid run around without supervision. (Also he knew one of the Kamacurus Mantises was still on the island somewhere, so even understanable ignorance of Kumonga can't get Goji out of this one. Unless being stupid is also part of his personality) Right down to teaching Minya how to do one thing, defend himself. Since, Godzilla doesn't actually seem to eat in the Showa series let's think of this as a stand in for hunting. Though while on that note, hell Minya even has to be fed by, either himself or the native chick, whom I forget the name of. It's not very fatherly of not to feed his kid. It's just animal behavior, and just like watching lions on the Animal Planet we personify them to be more like us.
I could write a rebuttal for KinGoji too, as he is also largely interpretive, but I'm honestly quite lazy and burn out from term papers