The BGV theorem shows that classical spacetime is past-incomplete, not that the universe began. Guth himself thinks the universe is probably eternal, and the theorem doesn’t apply where quantum gravity takes over.

That is the correct technical scope, in Guth’s own words: the theorem shows that inflating spacetimes cannot be extended into the infinite past under classical assumptions, and it says nothing about a quantum-gravity regime that might precede them. Vilenkin’s stronger reading, that the theorem combined with the failure of the main eternal models makes a beginning probable, is Vilenkin’s, and should be attributed to him rather than to the theorem. The claim survives in the form the leading eternal-universe models face a theorem-level obstacle, which is what the exhibit shows.