What country started out as a democracy?

I suppose it depends on how one defines "country".

When our continent was known on maps as "Australia del Spiritu Sancto" (I think I've got the Spanish correct) I doubt it could be called a country, as it had several hundred quite different groups of people living there, with little or no contact between many of the groups. When it was colonised by the British (most, but not all, of whom were English) its eastern seaboard was called New South Wales until separate colonies were established.

Matthew Flinders was the first to 'formally 'give the continent the name "Australia" after he'd completed its circumnavigation (1803, from recollection, when the British Crown was still very much in control over the colonial apparatus, Rum Rebellion notwithstanding) and mapped almost all its periphery but it wasn't until the late 19th century that large groups of people started referring to themselves as Australians. Government by 'relatively' democratic processes was in place in all the colonies occupying the country by that time and, when they were formally federated into the Commonwealth of Australia (New Year's Day, 1901) it was as a result of democratic processes

Perhaps we qualify.

Cheers, Rowan