How many possible outcomes are there for a 32 person competition that has 4 person matches where only 2 go on to the next round?

A coworker and I have a disagreement on this scenario.

There's a competition that has 32 contestants, and the first round consists of 8 matches that has 4 contestants each, and the top 2 people advance to the next round. (Getting 1st and 2nd matters as it depends where you're placed in each round; so does 3rd or 4th.)

Next round has the 16 advancing contestants with 4 matches, next 8 contestants with 2 matches, and so on. There are obviously $4! = 24$ possible outcomes for each match.

Where we disagree is that I believe there are $4!^8 \cong 110$ billion possible outcomes. My coworker thinks there are $$(24 * 8) * (24 * 4) * (24 * 2) * (24 * 1) \cong 10.6\,\text{million}$$ possible outcomes. We're probably both wrong, but we wanted to ask people who are likely smarter than ourselves. Thanks!

Assuming the structure of the tournament is fixed - so for example you know in advance that the winner of Match A will play the Winner of Match C and runners up of Matches B and D, in the next round etc., then there are $(4!)^8$ outcomes in the first round, $(4!)^4$ in the second, $(4!)^2$ in the third and $(4!)$ in the final.

This gives $(4!)^{15}=2^{45}3^{15}\approx 5*10^{20}$ total outcomes.