I don’t really understand why people are against using part of your time to study a science, art, or other intellectual field. Yes, I agree, learning Torah is the most important. But learning a science or art is NOT a waste of time. It is a wisdom given from G-d, and He wants us to appreciate and learn it as well. Learning science, in itself, I don’t think is bittul Totah. It may be bittul Torah when you put your science studies over your Torah studies, and give more importance to the former. Otherwise, I think G-d wants us to learn as much of the wisdoms that He put into our world as possible.
And I think one cannot say “You must finish x amount of Torah before learning science.” It is different for everyone. Some people need the “outlet” of learning another worldly wisdom in order to appreciate and understand their Torah learning more. Others may not need that extra stimulation and therefore can learn all of Shas before learning a word of science. I, personally, needed to delve into music and art in order to give me peace of mind and clarity when learning gemarah. I could not have done it without it.