Is it permissible to fulfill a vow to fast the first nine days of Dhul-Hijjah before the exam result, upon which the vow was contingent, appeared, knowing that the result later appeared as a success?

Whoever vows a fast conditional upon something happening, the fast is not binding upon them except when the condition is fulfilled. If they fast before that, it is considered a supererogatory act. A vowed fast is a physical act of worship that cannot be hastened, unlike financial acts of worship such as charity and zakat (definition). Therefore, your fasting before the exam results appeared is not sufficient, and you must fast the nine days of Dhul-Hijjah next year.