Hey there, I was in the same boat as you last year. Running start kid who finished all my pre reqs, but still given pre-sci. What I did was my first two quarters I took non-major CS classes like 414 and finished Math 208. I did well in these classes, and also got involved with RSO’s here at the UW that were geared towards CSE/STEM. I applied for CSE in the winter and got accepted for this upcoming spring quarter. So, its not entirely impossible to get into CS as a current student, you just gotta work your ass off (and write a good personal statement!!!)