Faith in God is warranted because God has provided three strands of evidence to make faith in Him reasonable. Your opening premise is thus skewed. It is after a person believes in the reality of God that faith is then needed to believe the promises of God and to live (or even die) for God. Faith believes and then acts. Plenty of people believe God exists but they have no faith that He has any dealings with humanity or requires anything of them, so they live godless lives. They do not believe the promises of God and that's where faith without evidence comes in but you have to believe He exists first! Abraham was no atheist: he believed God and acted, and that was counted as righteousness (by God) because he demonstrated faith in God. But his faith was needed to do what God required as Abraham had no proof that God would resurrect Isaac if he sacrificed him. That's where faith without evidence is needed - Hebrews 11:8-19. That whole chapter about people of faith nowhere says they had faith God existed; that's taken as understood because they went on to act in faith doing what God required. That's the point of biblical faith - believing God and acting in belief.
The 3 reasonable strands of evidence are, the work of God's hands - this universe, this planet, and all life on it. It bears His 'signature' as the artist who produced this magnificent work of glory which He gave us the brains to appreciate. Unfortunately, those who think brains developed inside the heads of little creatures in a pool of sludge seem to have no connection between their eyes and their vastly more complex brains.
Second, God broke into human history over the centuries, communicating with some people and even some nations. There are written records about that. Unfortunately, those who require newspaper articles, with photos of historic events, dismiss that written record as nonsense.
Third, God sent His Son to Earth, as a human, to do for unappreciative humans what they could never do to get right with God. Unfortunately, the faithless, who couldn't recognize God in Christ, crucified Him.
However, God resurrected His Son back to life, and over 500 people witnessed Him alive and well, during a 40-day period after His crucifixion Of course, that isn't good enough for people who have no idea what faith actually is. Why, even a Court of Law would accept the testimony of over 500 eye-witnesses (never mind if they could explain how it happened - they witnessed that it HAD happened. They saw the risen Christ!) A Court of Law would even accept circumstantial evidence that corroborated events. But not our faithless doubters! Oh no. They've got to see things with their own eyes, or see a video of it on YouTube, before they will believe anything.
Meanwhile, Christians just get on with declaring the good news about the crucified then resurrected Jesus Christ, the Son of God who makes God known to those humbly seeking Him.