Studying in the United States can completely achieve the purpose of immigration. China: Now, many international students get American green cards in this way.
According to the law, international students have 1 year to find a job after graduation. Through the employer's guarantee, they can change their student visas into work visas, and then apply for a green card after enough time.
I suggest you choose a major that is good for finding a job, such as engineering and liberal arts education. The difficulty of immigration has nothing to do with what university you attend. Now there are thousands of China students studying in the United States, and they all got green cards. None of them graduated from Harvard or Yale.