Is it permissible to raise the bid price in a project so that the engineers in charge can take a percentage, this being a condition for obtaining the project?

It is permissible for you to obtain the contract by paying a bribe to the engineers if no one better or more deserving than you is competing for it, or if you are more deserving of it. The sin falls upon the engineers. It is stipulated that you do not exceed the customary costs, as the Prophet, peace and blessings be upon him, said: "There should be no harm nor reciprocating harm." However, if there is someone competing with you who is more deserving of the work or equal to you, then it is not permissible for you to take the contract, and the engineers must fear Allah, for they are entrusted agents.