In that case, Corsica seems like it'd be a good bet, considering how close it came OTL. (
@Carp may have more)
This is probably the opposite of what you were expecting me to say, but I consider "Corsican Democracy" a bit overblown.
There is a long pseudo-republican tradition on the island, dating back to c. 1000 AD when the villages of the
Terra di Comune in north-central Corsica established a system of podestas and
caporali to unite against the southern Corsican lords. This does seem to have been an elective system, but we have little information on who did the electing. I presume that the villagers possessed a sort of primitive democracy, in which a small, economically-level community chooses its elders/big men/leaders. At most, the
Terra di Comune system formalized these choices and then established the framework by which these village leaders, in turn, could elect multi-village leaders that would be able to rally the forces of the whole region. It
sort of worked, but the communes nevertheless had to call the Margrave of Massa over from the continent to save them from the Count of Cinarca and his fellow aristocrats.
Presumably you meant the more modern incarnation of "Corsican Democracy" in Paoli's Republic, but the republic's democratic credentials are tenuous. The primary responsibility of the popular assembly, or "general diet," in Paoli's day was to get together once per year (in a place determined by Paoli), re-confirm Paoli as "the General," and then adjourn until next year. There's lots of faff in the 1755 constitution about courts, councilors, presidents, committees, and so on, but notably the General has absolute power over "affairs of war" in time of war, and given the fact that the Republic was in a perpetual state of war for the entirety of its existence there wasn't really much of a chance to test the capability, resilience, or independence (from the General) of these institutions. Famously, Rousseau wrote a constitution for Corsica at the invitation of Paoli and others in 1765, but there's no indication that Paoli or anyone else actually intended to follow his advice; they were essentially engaging in propaganda by associating their national liberation with the name of a well-known celebrity.
Paoli's government was, in effect, a charismatic "enlightened" dictatorship which possessed the trappings of democracy to legitimate his rule. That's not really a judgement on Paoli - the republic was always in a state of national emergency and it would be rather petty for me to criticize him for not being much of a democrat from the safety of my nice desk chair. Certainly the Corsicans did not begrudge him his power. I also concede that, compared to the political systems then in practice in most of Europe, Paoli's government (at least on paper) was at the vanguard of democratic governance. Since it only emerged a few years before the more thoroughly democratic United States, however, my guess is that it's not all that strong a contender for "earliest possible universal-suffrage republic."