How can a religious young man, who finds himself in great financial distress and debt that he cannot repay, and who engages in acts involving bribery within a corrupt system to earn a living which he considers tainted with the unlawful, find a way out of this situation, knowing that he has been unable to return the money he took from people with the intention of repaying it?

Your tribulation is a test from Allah, so be patient and seek your reward from Him. Obedience to a parent is only in what pleases Allah; he is not to be obeyed if he commands a sin. Freight forwarding services are permissible leasing. As for customs clearance and paying bribes therein, it is forbidden, unless you are compelled to pay it to avert injustice, in which case the sin is upon the one who takes it. If you find another source of livelihood free from doubts, then leave it. Otherwise, earning a livelihood from doubtful sources is better than begging from people. You must be patient and pious to succeed in this test.