Q: Why doesn’t God show Himself? Why do we have to believe in Him by faith?
Here are a few reasons that both individually & collectively explain why God the Father doesn't fully reveal Himself to all mankind. Though there could be other things as well.
A) Romans 1.20 explains that no one has an excuse not to believe in God because of the evidence of all He’s created. Reality confirms: The universe is vast, complex, well organized & well ordered (Job 25.2, Ps 19.1-4, 1 Cor 14.33). Some point out that the information in the universe (chemical sequences, genetic code, etc.) had to have had a programmer & would be impossible to achieve by chance, defying all probability & logic.
B) God has shown Himself by powerful miracles & inexplicable works in the past & people forgot or still didn’t believe (Ps 106.7-13). Reality confirms: Miraculous things still happen today, but most people dismiss them as coincidental & try to explain them naturally (2 Pet 3.3-7). Also, history has proven that people abandon God when distracted by their circumstances or prosperity (Dt 6.10-12, Num 14.2-3).
C) God operates on a different frequency so-to-speak. If you’re not tuned in, you won’t perceive Him (Isa 42.20, 43.19). Our sins (violations of God's perfect moral standard) scramble our signal & break off communications with the Almighty (Isa 59.1-2). Some people pray, but if they are loaded down with sin (see Good enough for heaven?), God won't answer. Reality confirms: Most people might claim they believe in or know about God, but they can't say they personally know God & do not truly perceive Him as they should. Many do not even believe in Him.
D) God is utterly holy, awesome & majestic (Ps 45.4, 93.1, Isa 6.1-5). His power is immense & unparalleled (Jer 10.6). If for some reason, God the Father fully revealed Himself to us, we would instantly die (Dt 5.25-26, Num 4.15.19-20, 1 Sam 6.20, Mal 3.2). Why? Because He is holy & just. He would require Himself to immediately punish all the evil things we have done (Zeph 3.8). Everyone has violated Him in some way (Isa 53.6, Rom 3.23, Jas 2.10). Reality confirms: God hasn't fully revealed Himself yet & we're still alive. You don't have to teach people to do bad, you have to teach them to do good. This is our default sinful nature that is opposed to God. Everyone has broken at least 1 of these 10 Commandments (Ex 20): Considered other things (religious or material) more important than God, Made God into who or what you want Him to be (idolatry), Used His name as a curse word, Failed to allot regular time to worship Him, Disrespected your parents, Hated someone (1 Jn 3.15), Lusted after someone (Mt 5.28), Stolen anything at all, Lied in any form or Greedily wanted what another had.
E) God even chose to take on the form of a man, Jesus Christ, & people killed Him (Ac 3.15). God used the sacrificial death of Christ to appease His justice so that if we believe that Jesus took the punishment of our personal sin, then He will forgive us (Rom 5.9, 1 Jn 1.9). Not only that, Jesus rose from the dead to conquer death & give us eternal life (Rom 5.10, 1 Cor 15.55), making us holy & good enough to stand before God ( 2 Cor 5.19, 21, 1 Pet 3.18). This was His ultimate display of love. Reality confirms: Jesus Christ was a real person who was brutally killed in Jerusalem by crucifixion (confirmed by non-Christian historians, like Josephus), came back to life & appeared to over 500 people (1 Cor 15.6). His grave is empty.
Though God doesn't fully reveal Himself to us for our sake, He does not want us to be ignorant about Him or what He requires of us, so He gave us the Bible, His written words (2 Tim 3.16-17) & sent His Son, Jesus (Heb 1.1-3), to make a way for us to be saved from our sins so we can enter His presence.
I figure that He always knew that it would take more than just "seeing & believing" (Jn 20.29), but graciously did & does show Himself in various ways. God doesn't perform miracles to entertain us, they are for His purposes. Ultimately, what really matters is what we believe & trust in our heart. Do you want to trust God on His terms (Rom 10.8-11)? It's not enough to believe in God, the demons even do that (Lk 8.27-28, Jas 2.19). No one can ever be "good enough" to get into heaven or appease His wrath (Isa 64.6, Mk 10.18, Rom 4.2). No one can hope or wish their way into heaven. Religion & rituals won't do it. No one can pray you into heaven (Ps 49.7-9).
1 thing is certain: we all must face God someday - either when we die (Heb 9.27) or when God does fully reveal Himself upon Christ's return (Rom 2.5, 2 Tim 4.1). It is not a matter of God threatening hell, it is a matter of our sin condemning us before an all-holy & Almighty God. Fortunately, God has made a way for us to be saved!!! (2 Cor 9.15)
"For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God's one and only Son." - Jesus in John 3.16-18
"Repent, then, and turn to God, so that your sins may be wiped out, that times of refreshing may come from the Lord, and that he may send the Christ, who has been appointed for you—even Jesus. He must remain in heaven until the time comes for God to restore everything, as he promised long ago through his holy prophets." - Acts 3.19-21
"For it is by grace you have been saved, through faith—and this not from yourselves, it is the gift of God— not by works, so that no one can boast." - Ephesians 2.8-9