How to deal with impatience when starting off in research?
From what you describe, i.e. preferring learning by doing rather than first getting strong theoretical foundations, you seem to be more a hacker than a academician. 

From Hackers and Painters by Paul Graham (whole essay is about this difference):


  The fact that hackers learn to hack by doing it is another sign of how different hacking is from the sciences. Scientists don't learn science by doing it, but by doing labs and problem sets. Scientists start out doing work that's perfect, in the sense that they're just trying to reproduce work someone else has already done for them. Eventually, they get to the point where they can do original work. Whereas hackers, from the start, are doing original work; it's just very bad. So hackers start original, and get good, and scientists start good, and get original.


In my personal case, impatience brought me from academic science to startup world and data science What I do or: science to data science. If I had know about my psychological traits, I wouldn't have dove into the academic world (it's not only about intellectual skills, but also patience... and ability to deal with hierarchy).