Your logic breaks down at step 2. As a counter example, what are the odds that in the other 7 weeks you would have zero cases? Of course the answer is that this

Your logic breaks down at step 2. As a counter example, what are the odds that in the other 7 weeks you would have zero cases? Of course the answer is that this isn't how the data works. You are not sampling a random, normally distributed event over a fixed interval, you are sampling the spacing between two different events where one of them is systemically linked to how you define the population and the interval.