There is a lot of variation in how PhD studies work. In some places, you are just a faceless candidate applying to a department, which discourages you from contacting the faculty before you are admitted. In other places, you must convince a professor to supervise and fund you before you are even allowed to apply. Some universities require you (or your supervisor) pay tuition fees for a number of years before you can graduate, while others don't care what you do, as long as you can produce a thesis that meets their standards.
You can jump from social sciences to STEM. Your formal admission can wait for a year or two after you actually started. Or you can move to another university and get a PhD in a few months, because the administrative requirements in the original one were too unreasonable. These things happen, because universities are independent organizations that like doing things their own way.
You can jump from social sciences to STEM. Your formal admission can wait for a year or two after you actually started. Or you can move to another university and get a PhD in a few months, because the administrative requirements in the original one were too unreasonable. These things happen, because universities are independent organizations that like doing things their own way.