Is it permissible for my family to open a restaurant that does not serve alcohol, but allows customers to bring their own alcoholic beverages and consume them inside, to ensure the project's success while avoiding the sale, purchase, and serving of alcohol?

There is no basis for the claim that trade is better than a salary, and the hadith "nine-tenths of sustenance is in trade" is weak. As for the suggestion of customers bringing alcoholic beverages into the restaurant, it is null and void according to Islamic law and forbidden. A Muslim is responsible for his restaurant and it is not permissible for him to allow sins to occur within it. The Prophet, peace and blessings be upon him, commanded changing evil, and whoever believes in Allah and the Last Day does not sit at a table where wine is circulated. Allowing forbidden acts in the restaurant makes its owners partners in sin, like one who allows adultery in a hotel. Therefore, it is forbidden to allow the bringing in and drinking of alcohol in the restaurant, and whoever fears Allah, He will make a way out for him and provide for him from where he does not expect.