No. The chances of this happening are extremely low. If a US based company is trying to hire in South Asia, almost certainly they’re trying to keep costs down.

Try to get as good a deal as you can during signing, and then renegotiate after to get an even better deal if you know you’ve provided that much value. Don’t leave money on the table.

The hiring market is insanely hot right now, don’t let it go to waste.