I think the intuition you need here is that while the size of the whale is bounded, the size of the infinite universe is not.(1) Thus the argument doesn't work, because the "faster and faster with each additional particle" assumption isn't met.

OTOH, your argument is a good one if we're talking about things like the entire infinite universe undergoing some transformation, provided that the probability of that thing happening somehow diminishes over time.

1) This is by far the best sentence I've ever written on Hacker News. So thank you! :)