Agree with Kisal, I think your best bet is to get rid of everything there, which will likely be mostly invasive exotic weeds and start over, planting native grasses and wildflowers.
Here's a couple websites to start with for that:
https://asgap.org.au/ (australian native plant society)
https://www.sgaonline.org.au/plants.html (sustainable gardening australia)
You do, of course, have other choices. You can continue as you are just stopping mowing and let the lawn grow out. As noted, you will have mostly your same lawn grass monoculture gradually more and more colonized by weeds. But we did that with a one patch of the lawn at my Quaker Meeting (church). Once the grass was grown out, we dug out small holes and planted in native wildflowers. Some took and some didn't and a few (goldenrod) have taken the place over. In our temperate humid area, we have to mow it once or twice a year to keep it meadow instead of reverting to forest. It still looks a bit weedy and unplanned, but very tall and thick and pretty in the fall when the goldenrod and some asters are in bloom.
Or instead of cutting the sod out, you could do sheet mulching (type that into Search the Forum, there's a lot of info). Scythe down or mow everything that's there so that it all lies flat. Then lay down many layers thickness of newspaper (water before and after the newspaper) and then lay down some inches thick of good topsoil on top of the newspaper, water, and plant into that. It's the same get rid of everything and start over idea, but less labor intensive way to desod. I did it to create a couple of small flower beds in my lawn and it worked beautifully.