how do you know your place is confirmed if you don't have an offer letter?
Anyway since you don't have an offer letter I will also assume that you don't have an eCoE. Without it you can not lodge a visa application and without lodging a visa application first you can not do a medical examination for an Australian visa. When you are applying for visa you will be able to see a list of places you can perform the checks and x-ray at. Choose from the panel clinics there and go. Life Care Diagnostics in MCIS Zurich near Hilton there is a good place. You can fill in answers online before you go for the check up and they will also submit results to immigration online shortening the processing time.
You have to apply for visa first and only then go for medical examination because you need your referral letter with the application's transaction number so the clinic can send your medical report to immigration. You CAN NOT do the medical examination for visa before lodging a visa application.

As far as DIAC is concerned, your eCoE is the only proof to you being accepted into any Australian educational institution as a student. And to obtain that you will first require a letter of offer from your uni.

Usually a blood test is not needed unless in certain circumstances where you probably have went to same dangerous level countries recently or got certain illness.

Just a physical examination, blood pressure, urine test and x-rays and this just require a few hours of your time.
The offer letter is not important. What immigrations want is the electronic confirmation of enrollment (eCoE) and you only get that after you get your offer letter, returned a signed response of offer to the university and have payed the deposit of tuition fees to the uni. After you do those stuff the university will usually send an acceptance letter and the eCoE within a week or so.

Anything pertaining to the Medical examination for an Australian Visa MUST be done at an Australian immigration panel clinic.