Intuitively, I feel that it is extremely more probable for a Big Bang, giving rise to life that knows science, to randomly occur than for a Boltzmann Brain, self-consistently simulating the evolution of such a universe for billions of years, to randomly occur. However, it is hard for me to explain that feeling more precisely.

Maybe it's like this: it is much more likely to randomly simulate a game of chess where a pawn gets promoted to a queen than it is to randomly generate a move history from random characters, which resulted in a valid chess game of a pawn getting promoted to a queen.