I hope all is well.
Law schools do not require applicants to have a specific major when applying to their law schools. For instance, an applicant can major in biology, history, civil engineer, nursing and apply to any law school. Typically, law schools look at an applicant’s GPA, extra curricular activities, LSAT scores, letters of recommendation, and interview skills if an interview is part of the application process.
The study of law opens up many doors for students. Many students who have undergraduate degrees in medicine, pharmacy, gerontology, or nursing choose to study law and end up practicing workers compensation, personal injury, or medical malpractice. Since you are an engineering major, you can go into patent law, civil litigation, contract law, or any other area that you might find interesting. You are not limited to just one area and once you are in law school you might find other areas that interest you such as wills and trusts, constitutional law, corporate law and even property.
If you are specifically interested in coming to the USA., your undergraduate degree, LSAT, and TOEFL should suffice along with letters of recommendation and your personal statement. You do not need to work as a paralegal or legal assistant prior to being admitted. It also depends on what the specific law school you are interested in requires. You can always visit the websites of schools that you are interested in and look at their admission requirements if you would like further clarification.
In addition, you may always apply for internships opportunities in big to medium sized law firms or even intern or work for a solo practitioner if you want more exposure. Also, you may contact your local court house and ask if they have any volunteer or intern opportunities for you.
Wish you the best of luck!