Was faith the absolute requirement for Jesus healing people?
"Now Peter and John went up together to the temple at the hour of prayer, the ninth hour. And a certain man lame from his mother's womb was carried, whom they laid daily at the gate of the temple which is called Beautiful, to ask alms from those who entered the temple; who, seeing Peter and John about to go into the temple, asked for alms. And fixing his eyes on him, with John, Peter said, "Look at us." So he gave them his attention, expecting to receive something from them. Then Peter said, "Silver and gold I do not have, but what I do have I give you: In the name of Jesus Christ of Nazareth, rise up and walk." And he took him by the right hand and lifted him up, and immediately his feet and ankle bones received strength. So he, leaping up, stood and walked and entered the temple with them--walking, leaping, and praising God. And all the people saw him walking and praising God. Then they knew that it was he who sat begging alms at the Beautiful Gate of the temple; and they were filled with wonder and amazement at what had happened to him" (Acts 3:1-10).
What faith did the lame man have? He didn't know who Peter and John were. He wasn't asking for healing, he was looking for money. Yet without asking and without faith, he was healed. A more accurate description is that faith came after he saw he was healed.
"Now when He had departed from there, He went into their synagogue. And behold, there was a man who had a withered hand. And they asked Him, saying, "Is it lawful to heal on the Sabbath?" -- that they might accuse Him. Then He said to them, "What man is there among you who has one sheep, and if it falls into a pit on the Sabbath, will not lay hold of it and lift it out? "Of how much more value then is a man than a sheep? Therefore it is lawful to do good on the Sabbath." Then He said to the man, "Stretch out your hand." And he stretched it out, and it was restored as whole as the other" (Matthew 12:9-13)
I find this one interesting because the man who was healed was a pawn in a play to trap Jesus. He wasn't looking to be healed, he had come to the synagogue for worship. He never asked for his arm to be restored. The leaders and Jesus were having a disagreement and then Jesus simply asks him to extend his hand. Jesus didn't even say what he was about to do, and yet the man was healed in front of a large number of people stubbornly holding on to their unbelief.
"Now it happened, the day after, that He went into a city called Nain; and many of His disciples went with Him, and a large crowd. And when He came near the gate of the city, behold, a dead man was being carried out, the only son of his mother; and she was a widow. And a large crowd from the city was with her. When the Lord saw her, He had compassion on her and said to her, "Do not weep." Then He came and touched the open coffin, and those who carried him stood still. And He said, "Young man, I say to you, arise." So he who was dead sat up and began to speak. And He presented him to his mother. Then fear came upon all, and they glorified God, saying, "A great prophet has risen up among us"; and, "God has visited His people"" (Luke 7:11-16).
Jesus and his disciples are just passing through. They are strangers here and happen to come upon a funeral procession. No one asked Jesus to do anything. No one was expecting him to do anything. He simply goes up to the widow to offer comfort and then tells the young man to get up. There was no requirement for faith. Nothing was offered to them to believe in until after the miracle occurred.
Just to show that it isn't unique to the New Testament:
"Then Elisha died, and they buried him. And the raiding bands from Moab invaded the land in the spring of the year. So it was, as they were burying a man, that suddenly they spied a band of raiders; and they put the man in the tomb of Elisha; and when the man was let down and touched the bones of Elisha, he revived and stood on his feet" (II Kings 13:20-21).
A man dies and as his friends take him to be buried, they see raiders approaching. Quickly they stuff the body in a nearby tomb, which just happens to be Elisha's. And when the body touched Elisha's bones, he was restored to life. No one was asking for a miracle. No one was looking for a miracle. Everyone's focus was on the Moabites and their need to defend themselves. There was no faith involved by anyone in this situation, and yet faith came as a result of the situation.
The congregation here went through the Gospels not long ago and I pointed out how often the miracles that occurred had little to do with the faith of the one being healed or the faith of those around. Miracles were not done for the miracle's sake. Miracles were done by God to produce faith in God and His teachings. "How shall we escape if we neglect so great a salvation, which at the first began to be spoken by the Lord, and was confirmed to us by those who heard Him, God also bearing witness both with signs and wonders, with various miracles, and gifts of the Holy Spirit, according to His own will?" (Hebrews 2:3-4). Sometimes the one being healed or the one asking for a healing was asked if he believed, but not always. But in each case the focus was on the fact that the healing came from God and it resulted in faith in God.