There are 3 universities that do not require UMAT I think. One is JCU but it requires a good application. Other is USYD and it requires 99.95 ATAR. Bond University is the 3rd one but its private university and costs a lot to go there.
To add to Best's list, no UMAT for USyd but requires 99.95, UMelb 99.90, Griffith 99.75-99.80 last year, Flinders ~99.85 (UMAT does count but only 10%).
There are 3 universities that do not require UMAT I think. One is JCU but it requires a good application. Other is USYD and it requires 99.95 ATAR. Bond University is the 3rd one but its private university and costs a lot to go there.