For four years the world had held its breath, but at last came the moment to exhale. Ever since noon on 20 January 2017, when Donald Trump took the oath that made him president of the United States, the people of the planet had found themselves in a state of heightened alert: what new madness might the most powerful man on earth unleash? Within months, he had seemed to threaten nuclear war with North Korea – in a tweet directed at Kim Jong-un, he boasted that “I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!” – and there were days when it seemed rational to wonder if America, and the rest of us, would even survive four years of a Trump presidency.

Eleven minutes before noon local time, it became possible to breathe out once more. Joe Biden recited the magical incantation by which a single US citizen is transformed into the head of government, head of state and symbol of the republic. As he uttered the words “So help me God,” his hand on a thick Bible, a wave of blessed relief rippled through millions of Americans – and all those, anywhere, who had lived through the stress of the Trump era. The TV networks had helpfully shown footage of the military aide who carries the nuclear “football”, the case containing the codes required to launch the mighty US atomic arsenal, and there was comfort in knowing that that aide now answered to Biden, not the man who a few hours earlier had fled to his resort in Florida.

Technically, the oath had come early. According to the constitution, the presidency was not fully in Biden’s hands until just after 12, and even those last remaining minutes were capable of inducing anxiety. “Phew,” tweeted one commentator when the moment finally passed.

But relief was not the only emotion on display in a ceremony performed before a National Mall packed with flags rather than people in an eerily empty Washington, hollowed out by both the pandemic and security fears prompted by this month’s storming of the Capitol. There was joy, too, most visible in the face of Kamala Harris after she had sworn her own oath. There have been 46 US presidents and 49 vice-presidents, but until Wednesday every one of them had been a man. Harris became the first woman, and the first person of African-American and south Asian descent, to occupy America’s second highest office. The elation of that moment, the exuberance of it, somehow found expression in the performances of Lady Gaga and Jennifer Lopez, which soared.

What would once have seemed ritual and routine acquired an emotional punch. The sight of Mike Pence on the platform was oddly stirring. Given his boss’s refusal to attend the inauguration, Pence’s appearance – and those of other Republicans – looked like an act of defiance, signalling acceptance of the democratic legitimacy of the proceedings. The presence of former presidents – Bill Clinton, George W Bush, Barack Obama – suggested the chain of American democracy remained intact, even if its most recent link was missing and broken.

That message was conveyed most eloquently by Biden himself. His speech was light on rhetorical splendour, but it matched the moment perfectly. It was like him: humane, decent, rooted. He asked for silence for those who had been lost to the pandemic, a simple act of acknowledgment that had eluded his predecessor. He named the challenges that confront him and the country – the virus, the war on truth, the climate crisis – and asked Americans to at least hear him out and come together. “We must end this uncivil war,” he said.

It was tempting to look on this man – solid and seasoned – and imagine that something like normality might return. And when another woman of colour, the 22-year-old Amanda Gorman, closed things out with a poem that brought delight, you could just glimpse a land that had been barely visible these last four years: an America the rest of the world might admire once more.