Companies don’t hire an international student because they want to be nice…
Companies hire an international student for one reason only: They are intrigued by that candidate’s potential value as an employee. Unfortunately, companies aren’t much impressed by the marketing pitch delivered by America’s universities on why international students make great hires (global perspective, language skills, diversity, etc.) There is a general dis-inclination to hire international students (of all fields) because of their need for an H-1B. Frankly, it’s easier to hire an American. This is precisely why the job search for international students needs to begin with an expression of value. And that value isn’t very compelling when its associated with a group of people (“international students”).
Employers (and specifically hiring managers), are only willing to hire an international student if they have been sufficiently convinced of the value that student can offer. In other words, the value needs to be pitched at the individual level for a specific role.
My recommendation is to forget that you need a visa for a while, and how companies feel about them, and focus on two things: 1. Being an excellent candidate, 2. Connecting with people who will understand that. Then let the mechanisms of the hidden job market take over.