Question

How was it possible for chemists to predict element properties back then?

Answer 1

How far back is "back then"? Before the periodic chart came into being by Mendeleev and Meyer (but Meyer has been largely ignored for his contributions) there was little to help predict properties. Newlands and others published some groupings but generally those were empirically done and the groupings came as a result of using known properties to make the groupings in the first place. I think the simple answer is that before Mendeleev we didn't have a good way to predict properties although followers of Newlands, Doberiner, and others may disagree.