Development of Omniscience

The Supreme Being of savage peoples is but an approximation to the ideal monotheism. There is a divergence, a difference of less and more, between what is postulated and what the data furnish, and all the efforts of the anthropological arguments to explain this difference as the result of a secondary degeneration or obscuration of the ideal presuppose the existence from the beginning of what does not take shape till later times and under particular historical circumstances. The whole theory springs from a compromise between historical investigation and theology. For the former, the attributes of Deity are not contained a priori in the monotheistic conception of God, for this conception is itself a formation, and the divine attributes likewise are formations, sharing in the development of the conception.
Raffaele Pettazzoni, The All Knowing God

The character “Yahweh” in the Hebrew Bible should not be confused with the god of western theological speculation (generally referred to as “God”). The attributes assigned to “God” by post-biblical theologians — such as omniscience and immutability — are simply not attributes possessed by the character Yahweh as drawn in biblical narratives. Indeed, on several occasions Yahweh is explicitly described as changing his mind, because when it comes to human beings his learning curve is steep. Humans have free will; they act in ways that surprise him and he must change tack and respond. One of the greatest challenges for modern readers of the Hebrew Bible is to allow the text to mean what it says, when what is says flies in the face of doctrines that emerged centuries later from philosophical debates about the abstract category “God.”
Christine Hayes, 5 Common Misconceptions About the Bible

The biblical writers and authors of other ancient Near Eastern texts described the divine person in anthropomorphic terms; later tradition defined specific divine traits (omnipresence, omniscience).
The Origins of Biblical Monotheism, Mark Smith

However, several of the earliest commentators of the Mishna already did not understand the phrase ha-kol safûy in the sense of ‘Everything is revealed and known from the outset’, but in the connotation ‘All that a man does in the innermost chambers, the Holy One, blessed be He, watches and observes’,11 and as Rabbi said, ‘Know what is above you—a seeing eye’ (M. ’Avot ii, 1); this explanation accords with the use of the stem safa in the idiom of the Tannaim. This verb does not signify knowledge of the future, but seeing that which exists and is present, like the Biblical usage ‘The eyes of the Lord keep watch [ sofôt] upon the evil and the good’ (Proverbs xv 3).
Urbach, Ephraim E.. The Sages: Their Concepts and Beliefs (Kindle Locations 5776-5783). . Kindle Edition.

Jehovah’s omniscience finds expression in connection with his omnipresence, and His ability to predict things. Because He is everywhere, He knows whatever occurs. He declares unto man what is his (man’s) inward thought (Am. 4:13). Hosea says, “the iniquity of Ephraim is bound up, his sin laid up in store”. Every sin committed by the people is present before God ; it cannot be lost as little as money kept carefully in a bag (Hos. 13 :12). God’s eternity comes into play here also. Being before all that happens, He has been able to foretell many things that came to pass, and now challenges the pagan gods to measure themselves with Him in further predictions (Isa. 41:22-24; 43:9-13; 44:6-8). This implies that His foreknowledge is intimately connected with His purpose. It is no magical divination of uncertain contingencies, but the natural concomitant of His plan. “Jehovah does nothing, but He reveals His secret unto His servants, the prophets” (Am. 3 :7). It is in vain to seek to hide one’s counsel from Jehovah, as the politicians try to do, who work in the dark and say: who sees us, and who knows us? This is in vain, because Jehovah is in reference to all plotting of man as the potter is to the clay: He fashions the very mind that conceives the thought of hiding from Him. Man’s hiding from Jehovah is an object of Jehovah’s own purpose (Isa. 29:15,16).
-Geerhardus Vos, Biblical Theology

Christian Platonism

In general, Ambrose shared the Apostle Paul’s low opinion of the ‘foolish philosophy’ of this world, but there was one exception: Platonism, with its unworldly emphasis. In a series of brilliant studies, the late Pierre Courcelle showed that phrases adapted and culled from the Platonist Plotinus are present in surviving texts of several of Ambrose’s sermons, those datable, probably, between 386 and 387.26
Fox, Robin Lane. Augustine . Basic Books. Kindle Edition.

Origen and Augustine are two giants – some would say the two giants – of the early Christian theological world. Each of them pondered fundamental questions of belief in a world marked by suffering and imperfection. For each the interplay of Divine justice, Providence, grace, human freedom and the love of the Creator for creatures was a problem that demanded a cosmic solution. Both addressed this problem with one eye on the Bible, the other on contemporaneous philosophical discussion. Addressing the most sophisticated critiques of Christianity, each contested the claim that later Platonism was most appropriately melded with traditional Greco-Roman religion rather than with Christianity.
The Influence of Origen on the Young Augustine, György Heidl

Although Augustine was greatly indebted to the great Neoplatonist philosophers, Plotinus, whom he regarded as Plato redivivus, and Porphyry, and although he insisted that they came to know God as the cause of existing, the source of understanding, and order of living, he also saw the limitations of these great philosophers who failed to recognize the work of Christ in his incarnation, life, death, and resurrection. Like much of what I have written on Augustine, the present article emphasizes his debt to the great Platonists for his concept of God and the soul as incorporeal or non-bodily beings and of God as non-temporal.
Robert Teske, Augustine of Hippo Philosopher, Exegete, And Theologian

The divine in the rabbinic documents is not presented as a transcendent, omnipotent or omniscient being, but a complicated, embodied, and fallible deity who evinces greater continuities with the capricious gods of Greco-Roman mythology than the incorporeal, unchanging Christian God of Augustine, Maimonides or Aquinas.
Rather than defend these odd and “embarrassing” anthropomorphic depictions of God as genuine expressions of the rabbinic imagination, the standard traditional Jewish response — from Moses Maimonides and on — was to neutralize the problem by adopting various strategies of containment. These apologetic maneuvers included de-canonizing or devaluing the non-legal sections of the Talmud and Midrash; seeing these strange divine images as mere “poetic conceits” for the uneducated masses; or embarking on various forms of allegorical reinterpretation that expose the deeper “spiritual kernel” of the rabbinic depiction.
The Protest Theology exchange, part 1: Judaism’s long tradition of confronting God, Dov Weiss

Greek v Hebrew Thought

The chief pagan god in the region that was to become Israel was El. El was male, patriarchal, a ruler. Unlike the other major god of the region, Haddu (the storm wind), El was not identified with any particular force in nature. He sat at the head of the council of the gods and pronounced the council’s decisions. The God of Israel was Yahweh. He, too, was male, patriarchal, a ruler, and not identified with any one force in nature. Rather than describing him in terms of nature or myths, the people of Israel spoke of Yahweh in terms of his acts in history—as we shall see.
Who Wrote the Bible, Richard Elliott Friedman

Divine being and divine action. This is another version of the same problem. Greeks appear to stress a theology of divine being, Hebrews of divine action. Writing of the structural problems which are intrinsic to the Christian doctrine of God, Christoph Schwobel identifies this one in particular: `the antinomy between the conception of the divine attributes in philosophical theology and discourse about divine action in Christian faith’.’ This is illustrated by a point often made by Robert Jenson, that there is a tendency to identify the divine attributes by a list of `omni’s’ and negatives – omnipotent, omniscient, omnipresent, infinite, eternal and the rest – and then paste on to them conceptions of divine action, especially that central to the Bible’s account of what is called the economy of creation and redemption: the temporally structured events in which God creates, upholds, redeems and will perfect the created world.
Colin E. Gunton. Act and Being: Towards a Theology of the Divine Attributes (Kindle Locations 222-227). Kindle Edition.

Semitic Concept of God

But of course, “God” as rendered in the Bible—and most particularly in the Christian Old Testament—does not conform to either the temptation of vagueness or the temptation of settledness. In contrast to both of these interpretive alternatives, “God” as rendered in the Old Testament is a fully articulated personal agent, with all the particularities of personhood and with a full repertoire of traits and actions that belong to a fully formed and actualized person. Such a particular person cannot settle for vagueness because the particularity has a history and an identity that remain constant over time. Such a particular person cannot accept a fixity as reflected in some forms of classical tradition, because this particular person possesses all of the dimensions of freedom and possibility that rightly belong to a personal agent.
An unsettling God – the heart of the Hebrew Bible, Walter Brueggemann

For the ancient Israelites it’s understood as a journey through time and space. Historically, we talked about the kind of God that the God of the Bible is; how he is, in fact, the god of this open future. And particularly he intervenes at moments of KAIROS – turning points where he tries to bring people back on course.
John Vervaeke, Lecture: Socrates and the Quest for Wisdom