I am a first year PhD student intending to work in convex optimization and its applications. I don't have an advisor yet, so I am still TA-ing. I had a long talk with a very helpful senior grad student in this field at my university today, and he recommended that I focus on taking lots of classes and learning a lot of mathematics for the first couple of years while working on small class projects and reading lots of papers in different areas, as opposed to trying to find an RA. He said having an RA means one is forced to work on one problem, and that doesn't let you explore on your own.
This is a totally new perspective to me. Until now I felt very ashamed of not having an RA, as I thought it reflected professors' lack of confidence in my capability as a researcher. Now maybe I am starting to see this as an opportunity to explore. However, I want to know other people's thoughts on this too; is it wise to spend the first two years just studying? He said that this would make life very easy for me about three years down the line when I am actually attacking problems. But I am just scared that this would be too late.
Do people in theoretical fields typically do this? Or do they learn on the fly? I don't want to be left behind and have regrets after two years at having taken things too slow now.