If this is a true gift, that is, not part of any larger transaction and given out of the kindness of your heart, then you're probably going to have to consult a tax professional because this will depend on the precise tax treaties between the United States and India.
Generally, when you give a gift to another person in the United States, you do not have to recognize the appreciation in value of that gift as a capital gain and the recipient gets the same basis you had, so they will have to pay capital gains tax when/if they sell it.
But generally, when you give a gift to someone who is not a US citizen, you do have to recognize the appreciation of the value of the gift as a taxable capital gain before you can gift it. However, this can be modified by tax treaties.
If this is not a true gift and is part of some other kind of transaction, then you absolutely must recognize the change in value of the bitcoin as a capital gain before you can give it to someone else, domestic or foreign.
Even if they know it was sold, how can they tax me as I am not the person who sold it?
The tax is not on the sale, it's on the increase in value which is a form of income. Generally, whenever you dispose of an asset, any increase in its value is a taxable gain. There are exceptions, such as a true domestic gift, those made by international treaty, and if it's transferred because of your death.