There are two gigantic problems with Ham's question. First, it severely underestimates the power of indirect empirical evidence. Just because we have to infer a conclusion doesn't mean the evidence used to do so can't be extremely reliable. If we have many pieces of evidence at a crime scene (blood, fingerprints, clothing fibers, etc.) at a crime scene all matching one murder suspect, that person is quite rightly convicted. The myriad converging lines of evidence for evolution mirror this scenario quite well. And in fact, the eyewitness testimony that Ham values so highly is notoriously fallible.
The second massive problem with Ham's argument is that it severely overestimates the reliability of the Bible. We don't have direct eyewitness testimony from God about creation; we have an ancient book written by people who claim to be speaking on God's behalf. As I wrote in this post, claims must be weighed in light of the quality of the source, not just the quality of the source's alleged source. And our source, as it turns out, is terrible: the Bible's errors, contradictions and atrocities make it highly unlikely that it was authored by an omniscient, omnibenevolent God.
I'll summarize by paraphrasing a response to Ham's question that I particularly like, which goes as follows:
Creationist: How do you know evolution happened? Were you there?
Evolutionist: I didn't need to be there. We have strong evidence from archaeology, biogeography, embryology, genetics and other fields that it happened. What evidence do you have for your position?
Creationist: God was there, and he wrote about it in his book!
Evolutionist: You mean the book riddled with evils, errors and inconsistencies? Do you have any evidence that God wrote it? If not, how do you know that he did? Were you there?