The God of the Bible exists. He has made Himself known through nature, Scripture, and His Son, Jesus Christ.
God has revealed Himself through His Word, the Bible. People can also know God exists by looking at creation (Psalm 19:1; Romans 1:20). The person and works of Jesus Christ are fundamental proof of God's existence. Jesus, God's Son, was with God at creation (John 1:1-3). The early Christian church certainly believed in God's existence. They had eyewitness testimony and evidence of Jesus' death, burial, and resurrection (Luke 1:1–2; 2 Peter 1:16), which they passed on to us through Scripture.
Supporting evidence for God's existence also comes from archaeology, science, history, literature, and human experience. There are ample reasons to believe in God; the real question is whether a person is willing to consider the evidence. But faith in God is more than an intellectual exercise. Faith comes from the heart. The physical evidence can tell us God exists, but faith is necessary to actually know God.
Is there a God? Every generation asks the question, and each person answers it one way or another. The truth is clear to those who seek it. Indeed, sometimes even avowed atheists change their mind. In 2008 the philosopher Antony Flew authored the book, There Is a God: How the World's Most Notorious Atheist Changed His Mind. In the book Flew discloses how his commitment to "follow the argument wherever it leads" led him to belief in an Intelligent Designer of the universe. However, Flew seemingly stopped short of acknowledging that Designer as the living God of the Bible.
Convincing scientific evidence and compelling arguments that the Intelligent Designer of the universe is the theistic God of the Bible is in a book by scientist-philosopher Stephen C. Meyer: Return of the God Hypothesis: Three Scientific Discoveries That Reveal the Mind Behind the Universe (2021, HarperOne).
Note that Christians distinguish between "God" and "a god." When Christians say "God," they do not include the indefinite article "a" before God. The God of the universe, the living God of Abraham, Isaac, and Jacob, is not one among many gods. Rather, when Christians say, "God exists," they mean there is One who is unique, who created and sustains the universe, who is immaterial and infinite, all-powerful, all-knowing, and all-present. God wants all people to be saved and to know the truth (1 Timothy 2:4).