Here in US analog IC Design is a unique skill, requiring extensive education and experience. Usually PhD and Post Doc efforts followed by many years gathering experience from "seasoned" colleagues is the typical path for most younger up and coming folks.
Best advice is stay in school as long as possible and push towards PhD, because once you leave and get a job you'll likely never complete the advanced degrees, and on the job experience will initially likely be mundane and not directly related to your keen interests. You'll need to wait years for the job(s) to come around to your true interests where you can lead the charge!!
This is the exact message I gave my Grad students when I was an Adjunct Prof long ago creating and teaching Advanced RFIC design courses. Few followed thru, most didn't, but can't recall a single student that returned to the classroom and completed the advanced degrees after leaving!!
Study the works of Widlar, Erdi, Nelson, Gilbert, Fullagar, and Brokaw, these are the True Masters of the Art of Analog IC Design in Silicon.
Another path is to master Analog Discrete Design with emphasis on Active Device Behavior and detailed Semiconductor Theory, after one becomes a true Analog Discrete Design master (many years active experience), then migrate into the IC design world (hopefully with the guidance of a seasoned IC designer) and prepare for entering a new world learning experience of IC design.
Best,