How can someone gift money to me in the USA from India without me having to pay taxes on it?

He can just transfer the money to you by whatever means is most convenient. There’s no US tax to pay on gifts received from abroad.

Money you receive as a gift is never taxable for you. It doesn't matter whether the gift is from another American citizen or a citizen of a foreign country.

If you receive more than $100,000 in the same tax year from a foreigner, then you must report this on your taxes, though it does not increase your tax liability.

For gifts or bequests from a nonresident alien or foreign estate, you are required to report the receipt of such gifts or bequests only if the aggregate amount received from that nonresident alien or foreign estate exceeds $100,000 during the taxable year. If the gifts or bequests exceed $100,000, you must separately identify each gift in excess of $5,000.

https://www.irs.gov/businesses/gifts-from-foreign-person#:~:text=In%20general%2C%20a%20foreign%20gift,and%20excludes%20from%20gross%20income.

If an American gives a gift of more than $15,000 to someone, then they must pay a gift tax on that:

The donor is generally responsible for paying the gift tax. Under special arrangements the donee may agree to pay the tax instead. Please visit with your tax professional if you are considering this type of arrangement.

For 2018, 2019, 2020 and 2021, the annual exclusion is $15,000.

https://www.irs.gov/businesses/small-businesses-self-employed/frequently-asked-questions-on-gift-taxes#:~:text=The%20annual%20exclusion%20for%202014,the%20annual%20exclusion%20is%20%2415%2C000.

Whether or not your cousin would have to pay any similar gift tax is a question for the tax laws in India.