What aspects of the problem of induction are simplified if you consider the problem using the B-theory of time?
A rough idea why this might be relevant:
First consider an urn with a finite number of balls in it. As I successively draw white balls from the urn, it is rational it increase my belief in the proposition "all of the balls in the urn are white". I do not think that this is controversial.
If you "sit out side of space and time" the set of swans in the universe is just a finite assortment like the balls in the urn. Thus, as you go through and sample them, finding each one white, you should increase your belief in the proposition "all swans are white" (up to the point where you find a black one).
There could be nits to pick with respect to the sampling methodology, i.e. we observe subsequent swans later in time, so if their color-state depends on the time we have a correlated sample; even so, our necessarily non-ideal sample still allow us to increase our belief in the global statement when you consider the process using the B-theory of time.