Slavic shares an ancestor with Baltic that could be called "Late PIE" or "Proto-Balto-Slavic", basically according to taste. It's not that these weren't developing or anything, and just magically popped up out of nowhere, but rather they're just attested quite late in the historical record compared to many other branches of Indo-European.

Proto-Slavic shows evidence of contact with Baltic, Iranian, and Germanic, wherever Proto-Slavic speakers lived, they must have been near enough to these groups to take words from them: it seems likely that the Dniester and the Dnieper form boundaries of Proto-Slavic settlement. As the Proto-Slavs expanded out, they displaced or assimilated people speaking Baltic, Germanic, Albanoid, Romance, Greek, and Finno-Ugric, depending on the particular location in question.