I am not sure how to prove a negative, it is unlikely that we will have it in Hegel's own words that he did not live at the end times. But the idea that Hegel saw his time as "the end of history" is not supported by modern scholarship. Dale in Hegel, Evil, and the End of History traces the fable back to none other than Nietzsche, namely to his Untimely Meditations:
“History understood in [the] Hegelian manner has been mockingly called God’s sojourn on earth, though the god referred to has been created only by history. This god, however, became transparent and comprehensible to himself inside Hegelian craniums and has already ascended all the dialectically possible steps of his evolution to this self-revelation: so that for Hegel the climax and terminus of the world-process coincided with his own Berlin existence...
Indeed, [Hegel] ought to have said that everything that came after him was properly to be considered merely as a musical coda to the world-historical rondo or, even more properly, as superfluous... instead he implanted into the generation thoroughly leavened by him that admiration for the ‘power of history’ which in practice transforms every moment into a naked admiration for success and leads to an idolatry of the factual.” [emphasis added by Dale]
According to Dale, Nietzsche’s “idolatry of the factual” alludes to “was vernünftig ist, das ist wirklich; und was wirklich ist, das ist vernünftig” in the Philosophy of Right, from which the Owl of Minerva also flies. But in fairness, Nietzsche explicitly describes Hegel as not saying what he "ought to have said", and even faults him for it.
As if Nietzsche’s scorn was not enough, the fable got additional boost after the Second World War. This part is traced in The Hegel Myths and Legends, a collection of essays edited by the above mentioned Jon Stewart, which has three, by Grier, Maurer and Harris, on "the end of history" specifically. The last two are well-known Hegel scholars, and Maurer even wrote a whole book Hegel und das Ende der Geschichte analyzing various meanings of "the end of history" and their applicability to Hegel.
"In France the lectures at the Sorbonne in the 1930s delivered by the Russian emigre Alexandre Kojève represent without a doubt the key event in French Hegel studies. Kojève’s provocative, yet at times fully misguided, interpretation was the main source of information about Hegel’s philosophy for the entire postwar generation of French intellectuals. The key figures of French phenomenology, existentialism, and Marxism, such as Raymond Aron, Maurice Merleau-Ponty, Georges Bataille, and Jacques Lacan, were all present at Kojève’s lectures and later developed the interpretation of Hegel that they received there in various directions in accordance with their own research programs...
Kojève seems to have borrowed heavily from the work of his fellow emigre, Alexandre Koyré, primarily with respect to the latter’s emphasis on Hegel’s purported claims about the end of history. These claims found clear affinities in the teleology of Marxist theory, where Kojève was most at home. The view that Hegel saw the end of history in his own time or with his own philosophical system has had its most widespread acceptance in France due to the influence of these two men. Although in the literature these problematic views have long since been corrected and revised by more thorough French Hegel scholars such as Hyppolite and Labarriére, nonetheless in the popular mind they are still quite pervasive."
Of course, the most recent burst of Owl's popularity is due to Fukuyama's The End of History and the Last Man, to which David Brooks, whose mention of the Owl prompted Pogge's answer, is likely indebted. And which in turn is traceable to... Kojève and Koyré, as Grier argues. If indeed Hegel had hopes of historical finality they were shaken by the French July revolution of 1830. On December 13 he wrote to his pupil Goeschel:
"At present the enormous interest of politics has swallowed up all others – a crisis in which everything previously dependable seems to become
problematic. So little can philosophy stand up to the uncertainty, violence, and evil passions of this great unrest, I hardly think that it can penetrate into those circles which rest so easily..." [quoted from Löwith's From Hegel to Nietzsche, p.28]
Not unlike Fukuyama's change of heart. Löwith has a long discussion of Hegel's "eschatology" and its historical context.