Faith can make all the difference between something happening and not happening. The Bible tells us that Jesus could do no mighty work in His hometown because of unbelief (see Matthew 13:57–58). God is sovereign. He can do whatever He wants whenever He wants with whomever He wants. He doesn't need our opinion. He doesn't need us to vote on it. He just does it.
However, the sovereign God that we worship and follow has chosen to primarily accomplish His purposes through human instruments. Now if I were God, I would not have made that selection. If I were God, I would just do things myself. Why mess around with humanity? We will only make a mess of things. But God has primarily chosen to do His work through people.
When God wanted to part the Red Sea, He didn't need Moses to hold up his rod. God was doing the work. But He commanded Moses to stretch out his rod over the sea, and the waters parted. God didn't need Elijah to pray for fire to come down from Heaven. God didn't need Noah to build an ark. He could have created His own ocean craft for the animals, Noah, and his family. But God worked through human instruments to accomplish His purposes.
It is interesting to note that Jesus did not heal everyone. But He did heal the ones who called out to Him, like the blind man who heard that Jesus was coming his way. He cried, "Jesus, Son of David, have mercy on me!" (Luke 18:38). Someone told him to be quiet, but that made him yell even more. So Jesus heard his cry, stopped, and that man was healed.
God responds to faith. Unbelief hinders the work of God, but faith unleashes it.