The analogy explains exactly what is wrong with your argument, which is that you point only to the total size of the space, without giving any indication of the fact that is relevant to how difficult it is to find what you’re looking for: The ratio of functions to nonfunctional things.
The total size of the space tells you nothing. Literally not a single thing. Whether it’s proteins in sequence space, photons in outer space, or Americans in America.
If the concentration of salt in a body of water is 0.1g/cm3 it doesn’t matter whether you have just one cm3 or a volume the size of the universe. Finding salt ions is exactly equally difficult. Blurting that there’s a lot of water is meaningless. The real question is the ratio of salt to water, not the total volume of water.
You’ve had this thing with the ratio explained to you many, many times before. I have a genuiinely difficult time convincing myself you don’t actually understand it. So why do you continue to pretend not to?
Guess what - there’s a wealth of evidence that there are enough such functional solutions to be found by evolution: