There is no idea or hint that there was any doubt that God would not provide a sacrifice—a substitute sacrifice. He knew that God had said, "and make him a burnt offering," but he also knew God.
At this point, he had maybe 50 years or so with God. God called him when he was 75. Isaac was born when he was about 100, and tradition says that Isaac was 33 when this occurred. It is hard to say. If that is the case, he had more than 50 years (about 58) of experience with God.
He knew God. He was God's friend. He knew that this was not something that God would go through with. Abraham knew the eternal, unchanging, holy, righteous character of God. He knew that God would not have him go through this horrid human sacrifice.
So, what did he have? We often look at this in terms of faith. It is a wonderful example of faith, but it is also a great example of hope, because the faith was the foundation for his hope.
You see, there was a promise that God had given him years before, and He said, "Your seed will inherit this land. In you the whole world will be blessed."
So Abraham put two and two together. "God has promised. I have one son who He said is the one that the seed would come through." He knew God. He bargained with God with the events in Sodom and Gomorrah. He got God down to 10, and God did what He said He would do.
And he had his own experiences with the birth of Isaac. He had gone to all those lengths to circumvent God, but God brought along Isaac exactly as He promised. So, Abraham had several examples to look back upon to see what God's character was, and then applied what he learned to this situation.
God tells him, "sacrifice your son," and Abraham says, "This all adds up." That is exactly what the book of Hebrews says about him—that it all added up.
What added up? God was not going to have him kill Isaac! He had hope that he would see his son live to be an old man (a father). So, he acted. He said, "Let's go. Let's do what God says, and God will provide."
He had hope. "Well, if God will have me kill him that will not stop God's promise. He could raise him from the dead. Isaac will live." There was hope for life. And so, he went through it.