Is it permissible to pay a sum of money to officials in the administration to obtain projects for the company, knowing that not paying may lead to the company's bankruptcy, and that the company is competent in its work?

The forbidden bribery is that through which one obtains what is not rightfully theirs. However, bribery through which a person obtains their right, or fends off injustice or harm, is permissible according to the majority of scholars. In this case, the sin falls upon the recipient of the bribe. If you are unable to obtain your rights or complete your tasks except by paying a bribe, and no harm results from it, then it is permissible for you to pay it, and the sin falls upon the one who takes it, and your money is lawful. Nevertheless, if you endure the injustice and do not pay the bribe, that is better.