Is the money earned by a father from his work in a supermarket that sells alcoholic beverages in America unlawful, especially since this is a condition for him to open his own supermarket, and he supports his family with it, and he has been unable to find another job due to not possessing citizenship or a "green card"?

Selling alcohol is Islamically forbidden and entails the curse of its seller, drinker, and everyone associated with it, as the Prophet, peace and blessings be upon him, said: "Allah has cursed alcohol, its drinker, its server, its seller, its buyer, its presser, the one for whom it is pressed, its carrier, the one to whom it is carried, and the one who consumes its price."

Therefore, your father must abandon selling alcohol and seek another job. Whoever fears Allah, He will provide a way out for him and sustain him from where he does not expect. Money earned from selling alcohol is forbidden wealth and must be disposed of by spending it on the welfare of Muslims. If it mixes with lawful money, the unlawful portion must be extracted. Performing Hajj with mixed money before extracting the unlawful portion is valid, but sinful for whoever knows that the very money used for Hajj is unlawful.