Short answer: No
Long answer: Any monster that is special summoned as part of a chain (Babbon's effect is an optional trigger effect and starts a chain) cannot be negated by Solemn Judgment. This is because, once the chain is resolving it cannot be interupted except by continuous effects or the effects of Archfiend monsters. So once Baboon's effect is activated, if the activation is not negated (Divine Wrath for example) then the special summon of Baboon is part of the resolution of the effect of that monster and Solemn Judgment cannot insert itself into the resolution of that effect.
I hope I've explained that in such a way as it's understandable.
