You should be a strong candidate for Direct to College admission at Washington.
See:
https://www.engr.washington.edu/news/direct-to-college
and
https://www.engr.washington.edu/admission/directtocollege/faq (which includes the following note regarding placement into a specific engineering major):
“Students who have completed all the course requirements for placement with at least a 2.5 GPA in those courses will be able to request placement into a major. Some majors will have more requests for placement than they can accommodate. The placement process will be facilitated to best match students with their interests. As part of an immersive first-year engineering experience, there will be many resources and opportunities for students to identify their interests and to understand multiple pathways for meeting their goals.”
Good luck!