Is it permissible to take a loan from an interest-based bank to purchase a taxi license due to the unavailability of an Islamic alternative and the high cost of other alternatives?

It is not permissible to purchase a taxi license or anything else through a usurious bank, because usury is one of the gravest major sins. However, since this has already occurred, you must hasten to pay off the installments, along with repentance, seeking forgiveness, and resolving never to return to dealing with usury. For whoever fears Allah and seeks lawful sustenance, Allah will provide for him from where he does not expect.