Well, the government technically could print a 1.8tn dollar coin with the sole purpose of paying off student debt
But the point you're missing is if student debt is canceled they don't have to make those payments back over one year but over the life of those loans. Further, we know from a 2020 report from the Trump administration that the government already expects to wrote off roughly 435 billion of the 1.6tn in currently outstanding student debt -- so about 1/4.
The average amount of time student debt is paid off is 20 years. So your concern is the government coming up with 1.2 trillion dollars over 20 years if it forgave ALL student dent or just a few hundred billion over 20 years if it forgave on 10k.
The government can afford it.