For a Turkish national, look here-
https://tr.usembassy.gov/education-culture/educationusa/
It will be easier for you to get to the USA for a PhD than for undergraduate education, but there could be options, to explore.
College of Wooster undergrad population is 15% international students, many on pretty good financial aid. Its also
known for undergraduate research. Its small, and you should get accepted. Maybe worth looking into this for neurosciences-
You have the list of highly ranked low probability schools nailed. What you need to do is find the smaller lower ranked schools that might want a student like you. You can always say no, and go to college in Turkey or Europe.