It depends.

In the Pentateuch, He is “God of my father,” “God of your father,” or “God of our father.” Their relationship to God is through the Patriarchs (Abraham, Isaac, Jacob/Israel). The Patriarch has a relationship with God, but they relate to God through the man, not directly to God. The Patriarch is the father of the nation (the Hebrews, Israel) through the Abrahamic covenant. A clear example is in Exodus. Moses wants to know who God is:

And God said to Moses, “I AM WHO I AM.” And He said, “Thus you shall say to the children of Israel, ‘I AM has sent me to you.’ ” Moreover God said to Moses, “Thus you shall say to the children of Israel: ‘The LORD God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you.”

In Judges, He remains Lord God of our (or their) fathers. But this changes a bit in Chronicles 22, when the son of David (and all after him) becomes a direct son of God:

9His name shall be Solomon, a for I will give peace and quietness to Israel in his days. 10‘ He shall build a house for My name, and he shall be My son, and I will be his Father; and I will establish the throne of his kingdom over Israel forever.’

11“ Now, my son, may the LORD be with you; and may you prosper, and build the house of the LORD your God, as He has said to you. 12“ Only may the LORD give you wisdom and understanding, and give you charge concerning Israel….

Same with 2 Samuel 7. Is this new God-as-Father to David’s offspring role part of the Davidic covenant? It appears so. See also 2 Kings 20 (“the God of David your father…”), and again when David commissions Solomon. Here, David appears to be the first to call God “our Father”:

10Therefore David blessed the LORD before all the assembly; and David said: “Blessed are You, LORD God of Israel, our Father, forever and ever. 11 Yours, O LORD, is the greatness, The power and the glory, The victory and the majesty; For all that is in heaven and in earth is Yours; Yours is the kingdom, O LORD, And You are exalted as head over all.

In Repentance Prayer (chapter 64), Isaiah declares, “You are our Father”. Isaiah is always operating in prophecy, always about Christ, always about the lineage of David.

In the New Testament, Jesus appears on the scene, not only calling God His Father (I and the Father are One) but also “Your father in heaven.” He commands the disciples to pray, “Our Father, in heaven…” But not all are His children. Some are “of your father, the Devil.”

Finally, Paul calls God “Our Father” and refers to the Church as “brothers and sisters in Christ” in every major new Christian doctrine he writes.

The Cross is not just an act of redemption, but adoption. He is our Daddy, not spiritual dictator.

This is an interesting progression and I do not recall seeing it studied anywhere.