Why doesn't God "prove" Himself to us so there is no need for faith?"
Our relationship with God is similar to our relationship with others in that all relationships require faith.
We can never fully know any other person. We cannot experience all they experience nor enter into their minds to know what their thoughts and emotions are.
Proverbs 14:10 says,
"The heart knows its own bitterness, and a stranger does not share its joy."
We are incapable of even knowing our own hearts fully. Jeremiah 17:9 says that the human heart is wicked and deceptive, "Who can know it?" In other words, the human heart is such that it seeks to hide the depth of its wickedness, deceiving even its owner.
We do this through shifting blame, justifying wrong behaviour, minimizing our sins, etc.
Because we are incapable of fully knowing other people, to some degree faith (trust) is an integral ingredient in all relationships.
For example, a wife gets into a car with her husband driving, trusting him to drive safely, even though he often drives faster than she would on winter roads. She trusts him to act in their best interest at all times.
We all share information about ourselves with others, trusting they will not betray us with that knowledge.
We drive down the road, trusting those driving around us to follow the rules of the road. So, whether with strangers or with intimate friends and companions, because we cannot fully know others, trust is always a necessary component of our relationships.
If we cannot know our fellow finite human beings fully, how can we expect to fully know an infinite God?
Even if He should desire to fully reveal Himself, it is impossible for us to fully know Him.
It is like trying to pour the ocean (seemingly infinite in quantity) into a quart-measuring jar (finite)... impossible!
Nonetheless, even as we can have meaningful relationships with others that we have grown to trust because of our knowledge of them and of their character, so God has revealed enough about Himself through His creation (Romans 1:18-21), through His written Word, the Bible (2 Timothy 3:16-17; 2 Peter 1:16-21), and through His Son (John 14:9), that we can enter into a meaningful relationship with Him.
But this is only possible when the barrier of one's sin has been removed by trusting in Christ's person and work on the cross as payment for one's sin.
This is necessary because, as it is impossible for both light and darkness to dwell together, so it is impossible for a holy God to have fellowship with sinful man unless his sin has been paid for and removed.
Jesus Christ, the sinless Son of God, died on the cross to take our punishment and change us so that the one who believes on Him can become a child of God and live eternally in His presence (John 1:12; 2 Corinthians 5:21; 2 Peter 3:18; Romans 3:10-26).
There have been times in the past that God has revealed Himself more "visibly" to people.
One example of this is at the time of the exodus from Egypt, when God revealed His care for the Israelites by sending the miraculous plagues upon the Egyptians until they were willing to release the Israelites from slavery. God then opened the Red Sea, enabling the approximately two million Israelites to cross over on dry ground. Then, as the Egyptian army sought to pursue them through the same opening, He crashed the waters upon them (Exodus 14:22-29). Later, in the wilderness, God fed them miraculously with manna, and He guided them in the day by a pillar of cloud and in the night by a pillar of fire, visible representations of His presence with them (Exodus 15:14-15).
Yet, in spite of these repeated demonstrations of His love, guidance, and power, the Israelites still refused to trust Him when He wanted them to enter into the Promised Land.
They chose instead to trust the word of ten men who frightened them with their stories of the walled cities and the giant stature of some of the people of the land (Numbers 13:26-33).
These events show that God's further revelation of Himself to us would have no greater effect on our ability to trust Him.
Were God to interact in a similar fashion with people living today, we would respond no differently than the Israelites because our sinful hearts are the same as theirs.
The Bible also speaks of a future time when the glorified Christ will return to rule the earth from Jerusalem for 1,000 years (Revelation 20:1-10). More people will be born on the earth during that reign of Christ.
He will rule with complete justice and righteousness, yet, in spite of His perfect rule, the Bible states that at the end of the 1,000 years, Satan will have no trouble raising an army to rebel against Christ's rule.
The future event of the millennium and the past event of the exodus reveal that the problem is not with God insufficiently revealing Himself to man; rather, the problem is with man's sinful heart rebelling against God's loving reign.
We sinfully crave self-rule.
God has revealed enough of His nature for us to be able to trust Him.
He has shown through the events of history, in the workings of nature, and through the life of Jesus Christ that He is all-powerful, all-knowing, all-wise, all-loving, all-holy, unchanging, and eternal.
And in that revelation, He has shown that He is worthy to be trusted.
But, as with the Israelites in the wilderness, the choice is ours whether or not we will trust Him.
Often, we are inclined to make this choice based on what we think we know about God rather than what He has revealed about Himself and can be understood about Him through a careful study of His inerrant Word, the Bible.
If you have not already done so, begin a careful study of the Bible, that you may come to know God through a reliance upon His Son, Jesus Christ, who came to earth to save us from our sins, so that we might have sweet companionship with God both now and in a fuller way in heaven one day.