My question involves a child custody case from the State of: New Jersey

New Jersey

I was living in NJ with my wife and 2 year 10 month old son.
Me and my wife are originally from India, I work here on H1-B visa and she was my dependent. My employer had filed for Greencard process. Our son was born here and is a US citizen.
Last week I went to Canada for work purpose, during this time my wife without informing me went away to India with our son. She just called from the airport saying she is leaving my house. I called her friend and found she had left for India. She left me a note at home saying that she was not happy with me as I didn't pay any attention to her and our marriage had no meaning. Had she discussed with me our marriage, I would have taken steps to solve the issue. But she never told me anything and took this extreme step of leaving me with my son without informing me. I am in complete shock.

I want my son to live a normal life with both his parents. I am willing to make adjustments if she comes back, but I know she won't because she is very stubborn and arrogant.

What are my legal options?
1. Can I file custody for my son here in NJ, as he is an American citizen and my wife has taken him back without informing me or without my permission? There is a point in filing for custody only if she has to come to US to fight the case. There is no point in filing for custody if she can ignore the notice, as she is now not in USA.
There is no point for me to file for custody in India, as I live in US.
2. Is a divorce necessary for filing for child custody? Should I file divorce here (we were married in India).
3. What is my best option?.

Kindly advice.
Avin