Yes, you can.
There are various testing sites on the Central Coast and you do not need a referral to get a PCR test. Alternatively you can do a home test with a Rapid Antigen Test (RAT). Stocks are currently quite low on these tests at the moment but will be easier to source by the end of January 2022.
The Department of Health is working on a program so you can self-report positive RAT self-tests by using the Service NSW app. This should be in place by mid January 2022.
Follow the Department of Health guidelines for a positive RAT self-test.