Why is it so important to God that we believe in him without any direct evidence of his existence? The Bible states that he parted the Red Sea and did all sorts of other miraculous things. The people who witnessed these events never had to rely on faith; they had the benefit of having his powers demonstrated to them first hand. If I were to witness the same things that these people saw, I too would be onboard with the whole thing. But no, I have to rely on words written in a book that obviously could have been made up by man. If you think about it, it is man that I must have faith in, not God. Is there something more than meets the eye with this faith thing; because, it sounds to me like just a convenient excuse when you dont have any hard evidence.
You raise a good question, however while you may have been convinced others would not be. For example there were still tons of disbelievers in the times of Moses and Jesus (peace be on both of them). Even after seeing with their eyes things that could not have been done or explained at all aside from concluding that God really exists, many people denied what they witnessed. They attributed many miracles to magicians tricks and maybe to their own gods if they could. So many times Jesus performed one miracle after another, only for people to see it and recognize it for what it was, then promptly deny the message Jesus came with.
Then the people of Jesus' time went on to demand that he show them Allah openly and plainly. Moses people demanded the same of him at one point. Not unlike many today demand that those who call themselves believers show them Allah/God openly and then they might believe.
So then what was their collective problem? Still even after you saw all that one still needed faith. Faith is the test. Can we believe in Allah without seeing Him openly? It's not a challenge to believe in things that your five senses can detect. I've found that the evidences for Allah's existence are circumstantial rather than completely concrete. By not showing Himself in a concrete way Allah is having mercy on the human being. If we had concrete, without a shadow of a doubt evidence we would not be able to disobey Allah for a single second without severe and immediate consequence.
From the Islamic pov this is what happened to Iblees/Lucifer/Satan. He had concrete evidence as he resided in paradise along with the angels. He saw Allah all the time and recognized Allah's complete authority over everything. However, Iblees possessed free choice as we do. He chose to disobey a direct order from Allah and thus was his fall. His punishment was swift and severe, and there was no option for forgiveness once Iblees decided to continue in opposition. The human family is not subject to such a horrible fate everytime we make a mistake or spend some portion of our lives in disbelief. The mercy in this is that Allah forgives us, based on the fact that we are relying upon our belief or faith that He exists and that He is worthy to be obeyed and worshiped.
This is why the people of that past had horrible punishments. They had great miracles presented to them in such a way, that disbelief was nearly intolerable. Everything from seeing the parting of the Red Sea, to hearing Allah speak to them. So when they decided that they would not believe, not obey Allah and His messenger, they were destroyed in grand fashion.
From an Islamic pov again, as Muslims we do not rely on the miracles that Prophet Muhammad (saw) brought. The trust and belief relies upon the way of life presented by Allah through all His messengers. The messages that Abraham, Moses, Jesus, and Muhammad brought are more enduring than the physical miracles they performed with Allah's permission.