Is it permissible to complete university studies through "wasta" (connections/nepotism) for someone who has been out of school for a long time?

What your father wants is intercession (wasaṭah), which is originally permissible. In fact, it is among the virtuous deeds that the Lawgiver commanded and encouraged. The Prophet, peace and blessings be upon him, said: "Intercede and you will be rewarded, and Allah will decree through the tongue of His Messenger whatever He wills." Intercession becomes forbidden if it leads to upholding falsehood or nullifying truth. We do not see any of that in what you have mentioned, so there is no harm in it.