From my understanding, there are very little companies that hire security consultants. Most of the security jobs also require some level of security clearance.

Entry level is your best chance but then again if you are on OPT it will be very hard to get into because most of the security companies do not have desi population thus not aware of sponsorship issues and mostly will be unwilling to do it.

Also security + is a very entry-level certification. You will need some sort of specific Vendor certification like Cisco / PAN / Juniper to the name the few. Security is a very big world, its like when you are trying to get into programming you will need to know specific languages and their frameworks.

Infrastructure, however, I believe are easier to get into as I see a lot of desis that work on it.