Ken Ham represents creationism, not Genesis 1.
The biggest problem with this debate before it even starts is that the claims Ham makes about the age of the earth are simply not claims the Bible makes. No Israelite theologian writing in the second (or first for that matter) millennium BCE would have cared in the least about the modern scientific questions regarding the age of the earth. To use genealogies to that end is misleading on so many levels, not least of which is the inherent endorsement of modern methods of apprehending truth, which are based on the modern assumptions about what truth is, despite the fact that those methods and those assumptions are built on the foundation of a naturalist/materialist worldview, which is a foundation floating on the ether of One gigantic metaphysical question mark.
In any event, and to the chagrin of the modern reader, the reality of this world as such finds much more ‘natural’ expression in literature that allows overlap in the genres of history and poetry, so while not all the Bible is classified in the genre of poetry, even its most wooden historical accounts have a poetic texture (von Balthasar, Theological Aesthetics: Seeing the Form), inviting the readers to think beyond the surface layer of its world, so that they might begin to think beyond the surface layer of their own. Of course, that is a terrible prospect, because if the Word of God rises from the world of the Bible that has been rendered a tomb of history, He may very well reach into the tomb of my heart and speak a binding Word in my world today.
Genesis 1 does indeed make the most audacious of scientific claims, and its audacity is compounded by the fact that it intends to give no scientific proofs. Most of us common folk really don’t know the evidence well enough to argue how old the age of the earth is without appealing to our faith in a certain circle of elites (religious or not), but frankly I don’t think it really matters, because Genesis 1 (and everything that follows) was not written to sit under the interrogation of secular scientists or of nervous Christian scientists under the interrogation of secular scientists. The Bible in General was not designed to sit under any of our interrogation while we demand from it whatever answers we so desire, as though we know the right questions to ask to lead us to the Truth in the first place (there was a tree back in Gen. 2-3 that should at least give rise to the question of the legitimacy of our desires). Unless we allow the Word of God to shape our questions, it will never satisfy our answers, nor will we be ready to hear the questions of Its response that intend to shape us. In the words of Karl Barth,
“What is there within the Bible?
“It is a dangerous question. We might do better not to come too near this burning bush. For we are sure to betray what is—behind us! The Bible gives to every man and every era such answers to your questions as they deserve. We shall always find in it as much as we seek and no more: high and divine content if it is high and divine content that we seek; transitory and “historical” content, if transitory and “historical” content that we seek. Nothing whatever, if it is nothing whatever that we seek. The hungry are satisfied by it, and to the satisfied it is surfeiting before they have opened it. The question, “What is in the Bible?” has a mortifying way of converting itself into the opposing question, “Well, what are you looking for, and who are you, pray, who make bold to look?”
Barth, Word of God & Word of Man
But to speak plainly, Genesis 1 simply cannot be understood for what it is trying to say, if it is read with the methods and aims of modern science. It should be heard in the way that a Hebrew slave would have heard it, after spending 430 years enslaved in Egypt, whose prayers to the God of their forefathers had turned into empty groans into the void of the heavens (Exod. 1); but who one day went to fetch water from the Nile and discovered blood, after which it started raining frogs (not men, hallelujah), then a bunch of other inexplicable phenomena started happening–and on and on it goes until they find themselves on the other side of the Red Sea, no doubt asking themselves three fundamental questions (the three fundamental questions that give rise to all cultural form and formlessness, harmony and chaos, Mozart and Nickelback): 1. Who is God? 2. Who are we? 3. And what does the One have to do the ‘others’?
Listen to Genesis 1 like that and then tell me what you hear when God says to these demoralized slaves (which is the fundamental state of all people in their sin) that they are essentially the culminative “very good” crown of his creation (Richter), made in the Creator God’s image, given dominion (slaves!), and blessed to multiply and subdue the earth–what kind of God is this generous?! Or you could just read it like a scientific textbook and get upset that secular institutions aren’t teaching your “Christian” cosmology contrived from your secularized interpretation of salvation history.
1. Genealogies after Genesis 12 are typically used to trace covenantal ancestral lines, which is why Abe’s, Isaac’s, and Jacob’s continue while Ishmael’s and Esau’s do not. But prior to Genesis 12 the genealogies still function to trace all people back to God (which is important for our later understanding of Christ as the ‘second Adam’, not the ‘second Abraham’; see Luke’s genealogy of Jesus, Lk. 3; cf. Rom. 5; 1 Cor. 15), which is in fact more of a statement about monotheism–Israel’s God is God of all, not some local deity among other deities–than it is about anything else.
2. Even if you hold to the Documentary Hypothesis or some totalizing historical reconstruction of the Pentateuch, the redaction is such that to give the literature its intended acoustic quality, it should be heard by the ears of a recently rescued nation of slaves (Deut. 1).