AHC - a Catholic White Russia?

Your mission, should you choose to accept it, is to create a scenario where White Russia (in the "more or less Belarus" sense, not Russian Civil War Whites) is an independent and predominantly Catholic state.

My first thought is to use the Time of Troubles, but I'm sure earlier PODs are quite possible. Later ones? I dunno. Thoughts?

If you mean 'more or less Belarus' in the cultural/ethnic sense then probably the best you could do would be a Uniate Church otherwise the POD need to prevent orthodoxy would have to be so far back that all of Russia and Ukraine would likely have to be Catholic too (conversion of Kievan Rus). To that end I'd say a more successful Union of Brest could result in a Belarussian Eastern Catholic (Uniate) state church. Then if the Partitions of Poland play out differently or not at all and Belarus remained under a Catholic power the Eastern Rite Christians could slowly start converting to a Latin Rite so that there's a minority Latin rite majority eastern rite Uniate population. Eventually 19th century nationalism leads to independence from Poland/which ever non-Russian Orthodox power controlled it.

If you mean Belarus merely as a geographic entity then there are lots of PODs that could work but would probably result in state that is culturally/ethnically Polish or Lithuanian/other Baltic.