If the school considers the summer as part of 2019-20 school year (prior) for financial aid, you’d complete that FAFSA and use 2017 taxes and assets as of the date of filing (2020). If the school considers summer 2020 as part of the 2020-21 school year (next), you’d file the 2020-21 FAFSA form and use 2019 taxes and current assets.
The only way to know is to ask the school.
You are not screwing up the next year by filing. You’ll file every year.
Make sure taking one class as a non-degree seeking student will qualify him for aid. It may be that the school uses FAFSA to qualify for state aid or the school’s own financial aid, but he likely won’t be eligible for federal aid like Pell or student loans.