...Or the scientific method.
Nonetheless, he does make a sincere effort to deal with the problem - while refusing to acknowledge that Sean Carroll is doing the same thing. The problem is that his solution effectively assumes what he is trying to prove - which leaves him in good company, since Boltzmann was forced to a similar expedient.
Of course, when the past is determined by the correct method – the method of retrodictions which is a form of Bayesian inference – we will find out that the lower-entropy states are exponentially favored. We won't be able to become certain about any property of the Universe in the past but some most universal facts such as the increasing entropy will of course follow from this Bayesian inference. In particular, the correctly "retrodicted past entropy" will more or less coincide with the "actual past" curve.
The secret sauce is the statement that in retrodictions
...the lower-entropy states are exponentially favored.
I'm putting that in my "remains to be demonstrated" file.