Let's ask two questions that are simultaneously similar, and yet radically different. 1. When did the dodo go extinct? 2. When did the t-rex go extinct? These two questions are similar because of their structure. Both are inquiries as to the time a certain animal went extinct. They are different, however, in that there are different ways of ascertaining the answer.
Of course, before we ask when each animal went extinct, we must first establish that they went extinct. The trouble with claims of extinction is that they're technically impossible to prove, and occasionally get disproven. Many species once thought to be extinct later re-appeared, alive and well. The coelacanth, for example, was claimed to have been extinct for 65 million years, until they showed up again in the 1930s. Thus, we can never really be sure that an animal is extinct. Nevertheless, we can alter our question slightly and ask when an animal appears to have gone extinct.
To answer this, at least as far as the dodo is concerned, we can ask when the sightings stopped. This is actually in dispute. The traditional date assigned to the dodo's extinction is 1662. However, hunting records kept by Isaac Joan Lamotius suggest a slightly later date (1). Ultimately, we can the last recorded dodo sighting was in 1688.
This is a simple matter of history. We gather the records, we check the records, we accept the records. The problem we have is that the further back in history we go, the shakier these records become. It's one thing to refer to hunting logs from 1685 - 1688 A.D., but you've got little hope of figuring out what life was like in 1685 B.C. That's not to say we know nothing, of course. It's just that a lot of evidence has disintegrated since then. We have less records from then, and we have less reliable records from then. Sometimes, entire cultures go missing (then occasionally show up again, sometimes confirming the Bible's reliability).
Now, if history that is kept by humans gets shakier the further back in history we go, meaning we have less knowledge about the 1600s B.C. than we do about the 1600s A.D., how shaky is our knowledge going to be about things that (allegedly) happened 65 million years ago? Answer: So shaky that not even Evolutionists can agree on it. They don't know how dinosaurs went extinct, they don't know when dinosaurs went extinct. They do have their stories (and as Greta Keller found out the hard way, they get quite religious in their defence of them) (2), but the fact is, due to the complete absence of records about dinosaur extinctions, we have no idea when the t-rex went extinct.
Of course, as Christians, we know the answer is nowhere close to 65 million years ago. But Evolutionists currently claim that is within the range. How do they know? The most interesting answer I've ever received is that there was a mass extinction around 65 million years ago that would render it impossible for such a massive carnivore to survive. But of course, that is rather circular reasoning. While I single out the t-rex in these discussions, it's because the t-rex is a dinosaur. The point isn't specifically about the t-rex, or even about the dodo. I could single out other animals that went extinct in known history, like the thylacine. The point is the strength of the historical record vs. the weakness of "scientific" guesses. Science is not about history, and so it is a less than ideal tool for making claims about history.
This is where Evolutionists typically bring up forensic science. There are two problems with this comparison. The first is that forensic science deals with known concepts. That is, they have been observed within human memory. Take, for example, the dating of a murder victim. Throughout the years, scientists have observed cadavers decaying under certain conditions. Thus, we can tell roughly how long a body has been dead by comparing it to those observations. Even this is not necessarily perfect, but it is at least reasonably accurate, because we have seen this going on. By contrast, no one has seen anything even remotely close to Evolution. We haven't seen mass extinction events, we haven't seen dinosaurs transitioning to birds, we don't even have reliable records that would contradict the Genesis account of creation, the flood, or the Tower of Babel.
The second problem with forensic science is that, as already noted, it isn't perfect. In fact, it all too often results in wrongful convictions (3). Now, I don't know about you, but if erroneous forensic science could have me wrongly convicted of a crime on the earth, I don't have enough faith in it to let it get me justly convicted of my actual sins before God.
And ultimately, that is what is going on here. The evidence was never the problem. The historical record cannot tell us when the last t-rex died, but it can tell us that Jesus died. It also tells us that He rose again, along with many other miracles with which He indisputably validated His claims to divinity. No one but the Author of life could have such power over death. And because of the power He demonstrated over death, you really ought to listen to Him, not only about where life came from, but how to secure your place in the next one. Only by confessing Jesus as Lord, and believing He rose from the dead, can we be freed from our sins (such as the blasphemy of Evolution), and instead inherit eternal life in God's Holy Kingdom. Therefore, repent, and be saved.
References
1. Hume, J., Martill, D. & Dewdney, C. Dutch diaries and the demise of the dodo. Nature 429, 1 (2004). (link)
2. Bosker, Bianca - The Nastiest Feud in Science, The Atlantic, What Really Killed the Dinosaurs, September 2018 (link)
3. Clark, Matthew - Faulty Forensics and Wrongful Convictions, Criminal Legal News, April 2021 (link)