There was nothing vague about God to Abraham. His relationship with God was of such intimacy that he thoroughly understood His character and purpose. He knew that he could trust God to act and react within clear parameters. Abraham added up what he knew about God and about His promise that Isaac was the promised seed, reached a conclusion, and acted. He knew God would have either to resurrect Isaac or to provide a substitute. He chose to trust the One he knew has the power and is faithful.
What if, like most Americans, Abraham had just guessed, based upon vague remembrances of a Sunday school class, movies, fiction works, and paranormal inspirations? We can assume that he would have worshipped the idols of his father Terah. A right concept of God is a Christian necessity because a wrong notion of Him is the very foundation, the starting point, for idolatry. In brief, the essence of idolatry is the entertainment of thoughts about God that are unworthy of Him.
God makes this clear at Mount Sinai after making the covenant with Israel and giving them His law. In Exodus 32, Aaron, confronted by the sinful pressure of his peers, became carried away and made a stupid Golden Calf to rescue them from their perceived dilemma. Aaron and the Israelites revealed that their false concepts of God remained. God had the idol immediately destroyed. Israel sinned in attempting to determine the nature of God based on their own reasoning, and many died in a punishing demonstration of the true God's wrath at this egregious sin.
The Israelites of today are still at it; modern Israelites are fantasizing about God. The idolater simply imagines a conception of God and then acts as though his conceptions are true. He is deceived and certainly does not know the true God as Abraham did.
God seeks out those with whom He desires to make the covenant. At that time, all they understand about Him is in broad terms. They are then to seek Him out to know Him more precisely. Those who make the New Covenant with God are required to seek out intimate details regarding His nature, purpose, and character.