This is a being we never see, never hear but has a major impact upon the Dresdenverse. We get hints in series and in WOJ, but here are my speculations.
(1) The White God stabilised reality by clearing the other major players off the board, some are in Demonreach, some are just gone, some knuckled under and agreed not to interfere in reality, staying like Hades in the Never Never, or taking a lesser role like Odin. It did this by agreeing not to otherwise intervene. Ethnui never agreed and hid until BG.
(2) as part of the agreement the White God established thresholds and the sunrise rule to protect humanity from the Supernatural, as well as the other limitations on Fae, vampires etc. We have evidence in universe as to Thresholds, Kringle can bypass them on Christmas Night without losing power or express invitation (Christmas Eve) even the Carpenters. He lunches annually with Uriel, servant of the White God, ergo the White God controls Thresholds, allowing Kringle through all Thresholds.
(3) Starborn, what little we know suggests this is a heavenly event, it is too contrived for it to be otherwise than on purpose, so this suggests that this is again another arrangement.
Perhaps the White God was powerful enough to take on all comers from either inside or outside reality, but could not win a war on two fronts, simultaneous attacks from Inside and Out. The Arrangements effectively mean the White God is pretty much policing them full time, and only really has Uriel, who can’t do anything to intervene in mortal realities.
We don’t see the White God because he does pretty much nothing, we don’t see the White God because he is doing pretty much everything.
Your final point is one that has been brought up by theologists before, and is certainly a plausible reason for the seeming lack of direct interaction from TWG.
TWG created everything, the whole Dresden Universe and all the parallel realities. Jim has flat out stated that several times. The Archangels are apparently on the level of major deities like Zeus etc. Odin perhaps would have been that powerful but chose (unlike Zeus perhaps) to give up most of his power in order to operate. Rather like how a wizard must give up most of his power at the threshold unless invited in. Perhaps that's the point. But Jim has effectively stated that all the other gods are below TWG, because the Creator made reality and because that was such an incomprehensible and amazing event even the gods get confused about what actually happened. I mean, before Creation cause and effect weren't a thing and neither was time. So TWG is above regular gods...but that isn't to say we really understand what that means. TWG could represent the Christian Almighty, the Hebrew God, Allah, Yahweh, El Adonai, Aten, Ahura Mazda and many others. But clearly is more than any of that. All those names represent concepts to try and understand the Creator being of the Dresdenverse perhaps and probably are just as right as they might be wrong. Jim said a whole thing on how the gods and other such powerful spirits (including TWG) and probably the Outsiders, are so big and powerful that humans can't really understand them and try and fit them into boxes and then get confused why it doesn't work and have arguments about it. He had a whole metaphor about 3 blind men and an elephant (google it if you need).
I don't agree that Ethniu "hiding" allowed her to escape notice and retain her strength. Remember, all the Gods and Proto-Gods were mighty once since the beginning even if they have retreated or been killed/imprisoned or lessened themselves now. Ethniu isn't Archangel level - although her father Balor (being the chief deity of a pantheon like Zeus) probably was. It was his Eye that could kill Uriel and other such beings. It isn't clear when most of the gods disappeared. I doubt it was one event but something that occurred slowly over time. Ethniu is simply the "last" (debateable) of the proto-gods or titans. I don't think there was a big sit-down meeting as such, I think it was more the endless fighting coupled with humanity's own changes that did it. Remember, Ethniu calls out how because humanity has progressed they have destroyed too many holy places and this weakened the divine, how humanity basically growing up meant that the gods were no longer quite as necessary as they once might have been.
The starborn cycle, and it's associated events (there appears to be one convergence of the stars that allows for the creation of starborn, and one that happens later that uses whatever starborn are alive - and Jim keeps hinting that it is pretty bad whatever it is) - I wouldn't think it's a "holy" thing. More like unholy. The first event happens every 666 years, and Jim has confirmed it is connected to Lucifer and implied it's connected to whatever Lucifer was doing at the beginning.
Also, TWG has 3 other Archangels to help him out (Michael, Rafael and Gabriel). Uriel might be the one WE see most, but we are often told he the one least seen. I suspect we haven't really been shown what the others get up to (although we do know that the Archangel Michael gave Sanya his Sword). But Uriel isn't alone. Also there are thousands, perhaps millions of angels also helping.
The reason TWG and other large beings don't show up is because reality and Creation can barely handle it. That's why we probably don't see TWG, or rather, we don't see TWG as we expect to. Gard makes a point about how Vadderung is merely a facet of the actual being that he represents, condensed down into something the mortal world and mind can handle. I TWG does something similar, and he is many orders of magnitude more powerful. Perhaps the Archangels are merely facets of the greater being that is TWG. Perhaps all the Angels are. Most people would expect a single being to interact with. But why? If TWG is all-powerful and omnipresent, why would there be a single point? In fact, by definition TWG would have to be everywhere and therefore couldn't have a single origin point. So even if a character talked to a being that called itself TWG or something like it...it would only be a fraction of itself anyway, by definition. Just a mouthpiece.