your only alternative explanation is “everything just happened randomly and here we are.”

Evolution is definitely not random. The mutations that show up are random, but the selection for them is very directed. If the traits give an organism the attributes to survive, it does and will pass those traits on. If not, it doesn’t. Your argument that it’s all random is typical creationist nonsense.

Neither approach, “intelligent design” nor “extremely long chain of random occurrences” can be empirically observed

We’ve observed evolution many many times. From the peppered moth to COVID and the flu, we observe evolution all the time. It’s the underlying science for all biology and none of it makes sense with out it.

Evolution is a theory that has been proven to be true over and over again. Intelligent design is unscientific garbage pulled from a book of fairy tales.