During the inter-war period, when Australians couldn't even vote for their own government, Bradman was the great Australian national hero. Australia was a colony, ruled from London, and locally by the Viceroy. Pounding the Poms at cricket was just about the only way that Australia could get one over the Mother Country, short of launching a revolutionary war. Hence the rapturous Australian response to Bradman's heroics.
Since then, John Ray has observed that "Australia became independent in 1901".
Sadly, I don't think either of them are quite right, although I htink John is closer to the truth than Brian. Australians certainly actualy got to vote for their own governments even well before 1901, but Australia didn't really become independent until several decades later. The issue of when Australia became independent is a complicated one. The following is a fairly long discussion of how Australia became independent with only occasional mentions of cricket, and some people may want to skip it. (I have still simplified parts of it, none the less).
I said yesterday that "There are two threads in (Brian's) post, one about cricket, the other about (essentially) Australian constitutional history. (I will post a separate piece on Australian history later). What I meant by this is that while I disagree with Brian, the discussion of just why I disagree is a lengthy one, and at the time I wanted to talk about cricket. I would argue that the various parts of Australia became self-governing between 1855 and 1870, but that Austrlaia did not become indpendent until about 1935. On top of that, cricket played a very important role in Australian nationalism, but it did that more in the 1880s and 1890s than the 1930s.
Australia was originally founded as a series of "crown colonies", ruled directly by governors appointed from London. As soon as the Australian colonies had substantial free (ie non-convict or freed convict) populations, this proved unsatisfactory to the local populations, and in most colonies a "Legislative Council" of wealthy citizens was set up to assist the governor in the first half of the 19th century. These arrangements also proved unsatisfactory, and starting in about 1855 what was known as "responsible government" was set up. (All the Australian colonies had this by about 1870). A second body, known as a "Legislative Assembly" was set up in each colony. These bodies were democratically elected, starting out with a property based franchise that broadened to a universal franchise fairly quickly. (Most of the Australian colonies had broader franchises than did Britain at the same time). Essentially, the Australian colonies has Westminster parliamentary systems in which their Assemblies took the place of the House of Commons and the Councils the place of the House of Lords. The Australian state governments retain this structure to this day (although the Legislative Councils are now generally also democratically elected).
Once the Australian colonies had responsible government, their elected governments had complete control over domestic affairs. (London theoretically could overrule them, but it never did). They taxed their populations, created a body of criminal law, ran the police, schools and postal service. They built the roads and railways. Once they existed, the governor had little to do but rubber stamp the decisions of the governments.
The problem of this system was that there were six of these governments. In particular there was great rivalry between the colonies of New South Wales (and Sydney) and Victoria (and Melbourne). Sydney was the older city, but Melbourne was the richer city. The Sydney establishment was in favour of free trade. The Melbourne establishment was protectionist. The states were unable to cooperate on anything. Most notoriously, the colonies built rail systems with different track gauges. This meant that to travel by rail from Sydney to Melbourne, you had to change trains at the border. (The reason for this was that the colonial governments wanted produce from their colony to be exported via the capital city of that colony, and having incompatible rail networks made this more likely). There were tarrifs on goods being transported from one colony to another. There was little sense of national Australian identity, but quite a bit of identification with particular colonies.
In 1876, a cricket team from England, featuring many of the best players in the world, visited Australia. It was taken as a given that local players would not be able to compete with the English, so the English team of 11 played local teams of a larger number of players to attempt to create a contest. The England team was beaten by a couple of these larger teams in Sydney and Melbourne, and it was suggested that perhaps a combined team eleven of the best players from both Sydney and Melbourne might be able to compete with the English on equal terms. Eventually, after much haggling between Sydney and Melbourne (Fred Spofforth, the great Australian bowler of the day, refused to play because the wicket keeper came from the wrong city) a team was selected and the game was played. To the surprise of a lot of people, the Australian team won. In 1882, an Australian tem beat and England team in London.
After this, combined Australian teams were regularly selected to play against England, and later South Africa. Therefore, Australia had a national cricket team when it did not exist as a nation. The cricket team was just about the first national institution. In this case, no excuses could be made, as Australia had beaten the best team England could put on the field, on English territory. In Australia, the celebrating was even greater. Nationalism due to cricket was a factor in the establishment of a national identity, that led to the constitutional conferences of the 1890s that led to the establishment of Australia's federal government in 1901. Cricket was not the key factor, but it played a role.
As mentioned, a series of constititutional conferences in the 1890s established that the rivalry between the Australian colonies was counterproductive, and proposed the establishment of a federal government to control those aspects of government for which it made sense to have Australia wide policy. A constitution was written, and the Australian colonies eventually all approved it by referendum. On January 1, 2001, the Commonwealth of Australia came into being.
The federal constitution that came into force in 1901 (and which is still in force) was a document written by Australian country lawyers, and was then sent to London to be ratified by the British parliament. There was an attempt to change it by some British parliamentarians before it was ratified, but the Australians absolutely refused to accept any changes. However, it was still a colonial document. The powers of the head of state are clearly divided into those of the "Queen" (ie the British acting directly) and the "Governor-General" (the Queen's representative in Australia, normally acting without reference to London). The G-G also is given the power to refer decisions to "The Queen", that is send legislation to London for the British to look at before it comes into force. These provisions for London to overrule the Australian government were not used even once, but the basic gist of all this was that although Australia gained a national government in 1901, and was certainly self governing, it could not really be described as independent. And it wasn't much more independent than the individual colonies had been before 1901. It had some national institutions, but not others. (Australia used the British currency until the 1930s, there was no separate Australian citizenship until the late 1940s, the highest court of appeal was in London until the 1960s, Australia did not really have its own foreign policy etc). In particular, Australia did not have independent foreign policy at this time.
I think in the few decades that followed the devotion of Australia to its sporting teams certainly did partly come from this "not quite a colony, not quite a country" status. Australians did get to vote for their own government, but there was some question as to whether that government was completely independent. Following the cricket team was much less confusing.
As to when Australia did become independent, subsequent to the Balfour Declaration of 1926, when Britain announced that Britain and its dominions (including Australia) would subsequently have equal status within the Commonwealth, Britain passed a law called the Statute of Westminster in 1931, which stated that Britain would no longer have to power to legislate for their self-governing former colonies. This is as good a date as any to give for independence (better than 1901, IMO), but even that is confusing, as Australia insisted that the Statute initially not apply to it. (Australia thought that if political ties to Britain were weakened, Britain would be less likely to protect Australia in the event of a war against Japan). Therefore, the Statute was written in such a way that it did not apply to Australia until Australia applied a law agreeing to it. Australia finally did this in 1942, shortly after the fall of Singapore had made it clear that Britain could not protect Australia from Japan and when Australia wanted to make it very clear that Australia would act in its own interests in the war). However for 11 years the situation was that Britain had granted Australia independence as soon as Australia passed a law accepting it, which it refused to do. In that time, in theory, Britain could have repealed the law granting independence, so whether Australia was independent or not was a point for the philosophers.
By the end of the second world war, Australia was clearly independent by any definition, and after the war in the Pacific in which the US came to our aid, our key foreign relationship was clearly with the US. The relatively few national institutions that were still missing (eg separate citizenship from the British) were established shortly. Various other colonial anachronisms have been removed at various times since. but these generally were anachronisms that didn't matter. (For instance, the Statute of Westminster in theory only applied to federal laws, and the state parliaments were in theory still subservient to Britain, and this wasn't fixed until 1986)