You've got to show the uni a TFN before the census date (31st March) otherwise your CSP place might be cancelled and you'll need to pay upfront I think
You should go to the Tax Office and apply for one (it takes a max of 28 (not 38) days to process and arrive in the mail). You can still get it in time before 31st March!

I applied for a tfn on 4th Jan and went to them the other day - they told me it'll come in the mail on 28th January (so sometimes it might take even less than 28 days!

And since you don't have it for now, just leave the TFN field in the enrolment form blank (I called 13MELB specifically about this, and they said nothing will happen if you leave it blank - i.e. your course won't lapse or anything) - Just be sure to get your tfn eventually and FILL THAT TFN FIELD BEFORE THE 31st MARCH