How am I, as a Christian, supposed to keep my belief in biblical inerrancy when there are all of these rebuttals that seemingly debunk creationism?
They don't debunk any creationism at any rate. Creationism is just another "science" but accepts the possibility that God is true.
More often, humans don't know what they are talking about. They are talking trash and BS including many posts in this very thread.
Basically, humans have two approaches to getting to truths. Science is the discovery of rule sets governing a repeatable phenomenon. Science is only accurate when humans can make that phenomenon repeat, and repeat predictably. It is so because humans lack the ability to tell a future. If a theory can predict precisely without error on how a phenomenon repeats itself into the future, we can be assured that the theory holds a truth. It is on a "you predict the future precisely that's why you are holding a truth" basis. That's what science is and why it is accurate.
Humans however literally call everything a science simply because they can't tolerate that they don't know things. Thus they literally name everything science in order to have an explanation for something they possibly don't know what it is. The "science" in this case however will no longer retain its accuracy as a predictable and falsifiable scientific model. Both ToE and BBT are such a theory that possesses zero predictability and zero falsifiability. That is, we can't theory what would happen in the next big bang, or in the next cycle of evolution from a single cell to a fully grown, say human.
We don't have the ability to predict how this process repeats in an end-to-end manner, simply because we lack the ability to actually make it repeat. We can't make a big bang repeat itself to achieve that said predictability and falsifiability. Similarly, we can't make a full cycle evolution repeat itself, that is, from a single cell to a fully grown human as ToE implicitly or explicitly said so. Our "science" in this case doesn't retain any scientific accuracy. Actually, the term falsifiability means "we humans can't tell if the theory itself is actually in error". If we can't tell whether something is in error or not, it could only mean that we can't tell if it's true either. This is a forever situation, that is, as long as we can't make it repeat, it is forever and eternally in such a status that "we can't tell if it is true".
The second more fundamental way for humans to approach truths is by means of human testimony. A scientist as an eyewitness observed with equipment that black holes exist, then his testimony reaches us for us to get to this piece of fact. We rely on this process of human witnessing because it is out of our capacity for the 7 billion humans on earth to go through the same process of observing through equipment to get to such a truth. We have to rely on this middle man (a scientist acting as an eyewitness) to get to the truth.
This is the case even on a repeatable phenomenon (i.e., a current physical existence), not to mention a non-repeatable phenomenon (such as a history).
Now since creation, if true, is not a repeatable phenomenon, the more proper way for humans to reach such truth is by means of testimony. However, it can't be a human testimony as no human is there to eyewitness the process. The only testimony can only be from God who remains the only one there to witness.
It is thus a situation where "God knows better" (thus He crafted the testimony), while "humans know nothing" as they think that the truth can be approached by science while science can only be in an eternal status that "we can't tell if it is true".
The next question is why even the most intelligent humans made such a mistake? The answer is, that even the smartest humans are not as crafty as the snake in the garden tempting them to eat from the Tree of Knowledge. A tree the same day you choose to eat from it, the same day you shall surely die! God not only knows better but also prophesied this.
The snake, on the other hand, is to fulfill the human need of knowing everything by calling everything science in order to have an explanation. This is done out of our pride.
