How does a young designer build taste?
Short answer
Depth is yours to find.
Long answer
The world will give you breadth. What the world cannot give you is depth. You have to find that depth for yourself.
We have an incredible amount of exposure today. The amount of material I consume in a day is what I would have consumed in an entire semester as a design student. So where does personal practice and your own identity come from as a designer? By going in depth, by practicing that one thing with depth.
When you are absorbing, you have to be patient. But when you are making, just make. Keep making, keep practicing, keep doing it again and again. Draw that one face fifty times, or draw fifty faces one time. Every one of those things will make you a better designer. There is no right or wrong to that. You have to find that balance.