A goodly amount of what is written in the Old and New testaments is wrong, or never happened, especially the Catholic versions. An example would be the dates of the Garden of Eden and the creation of modern man. 4,000 - 6,000 years ago is obviously incorrect, because we know that modern man has been around for at least 15,000 years, but likely a lot more. So if so much of the Bible, written by man, is false, how can one believe that it is "The Word of God"?
The Bible does not state how long ago the creation of Adam and Eve took place. People have used the chronologies in the Bible to try to approximate world history, but the chronologies are incomplete, and that presents challenges to any attempts to assign dates to events.
Because the Bible does not state “the dates of the Garden of Eden and the creation of modern man,” the charge that the Bible contains false and inaccurate information is unsubstantiated. Reasonable attempts to fill in the gaps of the biblical chronologies do place the creation of Adam and Eve below the time span you listed. Again, the Bible itself does not present a timeline of historical events with dates.
God certainly used people to write the Bible. Verbal inspiration means that the Bible writers wrote exactly what God wanted written down (1 Corinthians 2:13; 2 Timothy 3:16; 2 Peter 1:21). God himself is always truthful (Numbers 23:19), and what the Bible writers wrote is truth (John 17:17).
That last passage, John 17:17, explains that your complaint is really with Jesus. He stated that God’s word—not some of it, or most of it, but all of it—is truth. When the Holy Spirit convinces us of that, then we say what the psalm writer penned: “All your words are true” (Psalm 119:160). I pray that through the study of God’s word you come to that same confession.