Firstly, population density of the whole country is irrelevant. Population density of urban centres (e.g. Sydney + Melb > 10M pop.), is comparable if not greater than many cities in the US. We are largely self-sufficient for most food stuffs. I assume most of the US is too (I doubt that closing your borders would lead to empty food shelves). But we are entirely not self-sufficient for just about anything that's manufactured (the bulk of which comes from Asia, mainly China). We shut our borders to people (mostly) not goods. We also had governments that were willing to make politically very unpopular decisions based on the advice they were getting at the time. And the more the outcomes diverged between what we were seeing and what the rest of the world was experiencing, it became less politically damaging to make those kinds of calls (even more so because there was largely bipartisan agreement on the macro decisions even if details varied across states).

I live in Melbourne and went through 2 multi-month lockdowns. The first was 3 months, the second was 5 months. It may be comforting to think that it was "trivial" for us to control the spread of COVID, but I assure you it didn't fucking feel trivial 5 months into the 2nd lockdown.

It has nothing to do with population density. Other continents have fared much better than Europe, North America, and South America [1]. Many of the world's densest cities are on these continents.

[1] https://en.wikipedia.org/wiki/File:COVID-19_Outbreak_World_M...