I think the following:
USA: 1991-1996, After defeat of the USSR and before the rise of China and the muslim jihad, USA was alone and totally unchallenged.
UK: 1820-1825, The only industrial nation in the world, total naval dominance, de-facto largest empire (de-facto controlled India although they controlled it de-jure after the Sepoy rebellion) and the only place in the world that had functional railways.
France: 1680-1685, Before the war of the grand alliance, all enemies weakened (Spain,Austria,England), largest standing army in europe and navy rivaling England. Achieved religious consolidation well before England or the German stated.
Spain: 1525-1530, Held the largest empire including the newly conquered Aztecs and the futurly conquered Incas, humiliated France in Italy,had the best army in europe, England still rebuilding after the Rose wars.
USSR: 1955-1960, Overtaken USA scientifically and diplomatically, had advantage in ICBMs (USA didn't have ICMBs), first man in space, all third world worshipping it.
Russia: 1780-1785, Catherine the great dominant in Europe, England lost america and france is moribund.
Ottomans: 1526-1531, After the conquest of Hungary and the Arab countries.
China: Probably 1415-1420, New vigorous rulers, all enemies crushed, total naval dominance and total weakness of every other power (Ottomans, Mamelukes, Mongols, Delhi sultan, European countries). I don't believe China will achieve anything comparable to that.
Rome: 117-122AD, During reign of Trajan, Largest extent of the empire, all potentional rivals (Parthia, Germanic tribes, internal rebels) weak or non-existant.
Germany:1875-1880, Crushed France, Economic powerhouse, Best army in the world and diplomatically dominant (good relations with everybody except France)