Apart from BA, no European airline fly's to Australia, they can't compete with all the hub airlines in between which have lower costs and offer stopovers.
Any time of the year will be off season somewhere with that country's airline offering seats at break even prices just to fill them. Even QF had such a hard time competing that they had to partner with EK.
The Middle East 2.5 can offer a 1 stop connection from most Australian capital cities to most cities in Europe at a decent price and many of the Asian airlines can do the same, often undercutting if they have a sale on.
Some SE Asian destinations might be worth looking at via a Darwin hub as many of these airlines have restructured due to COVID and dropped everything except Sydney. Brisbane to Phuket requires a connection somewhere and DRW might work.