I have many missed fasts from when I was younger and not a practicing Muslim. I found out about the kaffarah that must be paid for each day I missed. Since it is a lot of money, my father offered to help pay for it as I am still a student and dependent on his income. Is this permission or do I have to get a job and earn the money myself directly?

Yes your father can give you that money and then you make the intention to pay Kaffara with it. You do not have to work yourself and earn that money. Someone else may give it to you.
By the way, scholars have said if you really didn’t know that fasting was mandatory when you were younger, then you don’t have to pay kaffara. But if you knew it was mandatory and out of negligence you deliberately didn’t fast then you pay kaffara.