I will make the thought-experiment of imagining myself as being this Omni-God, having made creation - and desiring now to make Men who would have genuine individual agency.
Clearly, it would be useless to make many Men and control all of them directly - because that would simply be to make a puppet show.
But a more common argument is that God made Men and placed within each Man a small portion of himself - a 'divine seed' - and it is this divine seed within each Man that enables him to be a genuine free agent; to think and choose independently from God.
But this does not work either! If the direct-control God would just be a kind of puppet master - this 'remote-control' God would just be a kind of playwright, whose characters only superficially appear to be agents.
If God makes all the ingredients, then no matter how these ingredients are divided and mixed - every-thing is still God. All agency is still God's.
Thus, a Man whose agency depends on a divine seed from the Omni-God is still the Omni-God - albeit just a part of that God - like a character in a play is always a part of the playwright.
Thus, a dramatist can make a play with twenty different, and differently-motivated, characters... But ultimately all of these characters are just fragments of the playwright's own character.
Their differences do not make the characters have free will - each is still 'inside' the play. Likewise the fragments of an Omni-God do not have agency - each is still inside the creation, All of which has been made by Omni-God.
The Omni-God may then try to make his 'characters' develop agency - even if they did not have agency to begin with...
He might reason that - even though each character in his play begin as just a fragment of God; by interacting with his environment and by learning, each Man will potentially develop independence of will - and will learn agency.
This would be analogous to the playwright setting-up his drama with characters - each a fragment of his own character - but then as the play proceeds, the characters will interact and experience events in unexpected ways that might surprise the playwright - and were not predicted by him.
The characters 'become real' to the author, 'take on a life of their won' - as writers sometimes say...
But that is just another superficial illusion in the case of the Omni-God; because all possible interactions between all Men and all environments are still just a part of God. And even the capacity to learn from experience was a quality implanted by that same Omni-God.
Furthermore, the Omni-God already knows the result of these innumerable interactions, because he is omniscient - so he will not even experience the surprise of a human playwright!
So, it turns out that the Omni-God does not generate agency; whether as a puppet master or as a playwright.
When no individual 'human agency' goes-into the mix of creation; and when all of creation comes from the Omni-God - then no amount of dividing and mixing and interacting can make human agency emerge from creation.
My inference is therefore that if human agency is real - as Christianity requires it must be (and if this thought experiment is valid*); then the Christian God cannot be an Omni-God.
For human agency to come-out-of creation - human agency must have gone-into creation.
Note: the intention of this thought experiment is to clarify my argument: to make it more comprehensible. Of course, it does not prove anything - because no thought-experiment can prove anything! But it may lead to an understanding of the argument explaining why there is no way to get personal-agency out-from the assumptions of an Omni-God; and why Christians for whom the issue of free-will/ agency is primary (and who are not happy that it should be regarded as wholly an incomprehensible mystery) therefore need to discard the Omni-God concept.