If I pull two clubs in a row out of a deck of cards, the whole deck is clubs in my view, and no amount of math will convince me otherwise. As you would have me understand it, the size of the sample has nothing to do with it.
How does this example work out mathematically in comparison with the amount of earth exposed for scientific observation and analysis?
Las Vegas was built on people with your understanding of probability (but with a greater propensity to gamble though.) The probability of 1 club is 13/52, if you draw without replacement the second club has the probability of 12/51; multiplying gives 156/2652 or about 6%, not rare.
Of course, using your reasoning about cards, as all examples of geologic columns support the conventional view, the whole Earth is described by the conventional geology. After all, the second sample agreed with the first, as did the third, and the thousandth.
You are confusing sample size with population size. The sampling error depends on the sample size, but not the population size (for large populations). In the example you gave, the sample size you use certainly matters. In your example, it makes no difference though, whether you are using a 52 card deck or a 52000 card deck, your conclusions are the same.