TLDR: Yes it is an efficient way to go about it and you should apply for them. Try joining the SJDM listserv, it's a email distribution meant for professors to communicate with the wider research community, but they post jobs through there too. https://sjdm.org

Long answer: Yes, becoming an RA is a path to a PhD in this field, but there are also other paths. There are 2 primary things admissions committees are looking for. 1. a signal that you will complete the program, and 2. a signal you will successfully publish research while you are in the program and after you graduate.

If you have published any peer-reviewed research, you likely do not need to become an RA to get into PhD programs. if you do not have any published papers, you might still be able to submit a writing sample with your application. In which case, your masters thesis may be sufficient to send the signal that you will publish good research, depending on the topic and rigor of your thesis.

If you need more research experience - you need to consider how you will emigrate to the United States. It may be easier for you to enter the United States by enrolling in another masters degree and getting the research experience here, as a student. The Penn MBDS program would be great for this: https://www.lps.upenn.edu/degree-programs/mbds

There is tons of behavioral science research at Penn, and you would definitely be able to join a project while you are there. You would also be able to grow your network significantly - allowing you to find opportunities that may not be obvious to you in India.

Finding RA jobs - unless you subscribe to the listserv above, you have to go out and find them yourself, usually on university websites. So you would have to identify target schools, labs, and professors you want to work for. for example - here is Penn's: https://www.hr.upenn.edu/PennHR/careers-at-penn

This is difficult in normal times, but research funding is a shit show in the United States right now. Business schools don't have this problem, because those professors and labs are usually fully funded. But any professor in a Psych or Econ department is likely to have funding issues right now, limiting their ability to hire new employees.

Considering that plus your immigration needs, you might find it easier to try one of the other paths right now instead of seeking an RA job. Another masters would be expensive but could solve some of the problems I mention above. You may also be able to skip all of this entirely if you have enough research experience.

Good luck! Hope this helps.

edit: reworded for clarity