Unlike the Hindenberg wreckage, we do have access to much of the past. Every fossil is a piece of wreckage, if you will. The geological strata are wreckage. Ice core data is marvelous evidence. Radiometric dating provides evidence. Tree rings are evidence. Molecular DNA analysis is one of the newest tools giving us phenomenal new insights. No doubt we could have much more data than we do, but there is still plenty of data from which to draw persuasive inferences.
What do fossils prove? They prove that the animal died. That's all. You don't know that animal had any offspring. You certainly don't know it had offspring different from itself.
With regard to geological strata, trees have been found standing up and passing through multiple layers. This throws a spanner into the works for the evolutionists, who believe the layers are different ages.
Radiometric dating is based on several assumptions that are untestable. We don't know how much carbon-14 was originally in the organism being tested. We don't know if the decay rate has always been the same. I remember seeing a programme about radiometric dating and it showed a couple of forms that were filled out in order to get something dated. One of the fields was "expected age". I have heard of specimens being re-tested because the age given doesn't fit with the evolutionists' time scale.
You are formally correct that proving possibility is not proving actuality. However, the issue is really probability. Forensic sciences rely on abductive reasoning, reasoning to the best fit. There is nothing wrong with this process. Furthermore, there is no philosophically meaningful distinction between "historical" science and "observational" science. No philosopher of science would grant such a distinction, nor is there any reason to do so. It is certainly not the case that the conclusions of "observational" science are always more secure than "historical" science. For example, I am much more sure about the fact that George Washington was the first president of the United States of America than anyone is about whether light is a wave and/or a particle, something that has been the subject of countless experiments.
I know evolutionists don't like the terms 'operational science' and 'historical science'. But there
is a fundamental difference between them. With operational science you can conduct experiments to test hypotheses and demonstrate that they are true. However, you can't directly study the past because, well, it's in the past. You can only do experiments here in the present and assume that the conditions in the past were the same as they are now. This is called uniformatarianism (the present is the key to the past), and it is foretold in 2 Peter 3.
"Know this first of all, that in the last days mockers will come with their mocking, following after their own lusts, and saying, “Where is the promise of His coming? For ever since the fathers fell asleep, all continues just as it was from the beginning of creation.” For when they maintain this, it escapes their notice that by the word of God the heavens existed long ago and the earth was formed out of water and by water. (2 Peter 3:3-5)
The difference is ultimately your worldview. The facts for creation and evolution are the same. The creationists approach those facts with a Biblical worldview whereas the evolutionists approach the facts with a naturalistic, materialistic worldview. For example, it is a fact that there are layers of rock seen in various parts of the world. The creationist sees these layers as being laid down during the Flood mentioned in Genesis. The evolutionist sees these layers as being laid down over long periods of time. However, the evolutionists are always trying to erase the line between the fact and their own interpretation of the fact.
Also, proper science allows theories to be tested and thrown out if serious problems are found. Evolution isn't treated like that - it's the Holy Grail of the materialist scientists and woe to anyone who threatens to question it. Academics have lost their jobs from announcing that they don't believe in evolution. Do you think that grant money would be given to a project whose objective was to disprove the theory of evolution? I doubt it.
This is not science. This is dogmatism.
