On 21 July, when Joe Biden announced he was dropping out of the presidential race and endorsing Kamala Harris, the dream of seeing a woman in the Oval Office was suddenly back within reach. It wouldn’t be me; but it could be Kamala. History beckoned. But a whole lot of bigotry, fear and disinformation, not to mention the electoral college, stood in the way. Could we do it? Could we finally shatter that highest, hardest glass ceiling and prove that in America there is no limit to what is possible?

When Bill and I heard the news that Biden was withdrawing and endorsing Kamala, we drafted a joint statement saluting him and endorsing her. She is talented, experienced and ready to be president, so it was an easy decision.

After our statement went public, Kamala called us. She was remarkably calm for someone who had just been thrown into the deep end of a bottomless pool. She told us she wanted to earn the nomination. “I’m going to need your help,” she said. “We’ll do whatever you need,” I told her. Bill and I were both ready to do everything we could to help get her elected.

History is full of cautionary tales, but 2024 is not 2016. Trump’s victory then, and the ugliness of his presidency, woke up a lot of people. There’s less complacency now about the strength of our democracy, and more consciousness of the threats posed by disinformation, demagoguery and implicit bias.

Some people have asked how I feel about the prospect of another woman being poised to achieve the breakthrough I didn’t. If I’m being honest, in the years after 2016, I also wondered how I would feel if another woman ever took the torch, that I had carried so far, and ran on with it. Would some little voice deep down inside whisper: “That should have been me”?

Now I know the answer. After I got off the phone with the vice-president, I looked at Bill with a huge smile and said: “This is exciting.” I felt promise. I felt possibility. It was exhilarating.

When I imagine Kamala standing before the Capitol next January, taking the oath of office as our first woman president, my heart leaps. After hard years of division, it will prove that our best days are still ahead and that we are making progress on our long journey toward a more perfect union. And it will make such a difference in the lives of hard-working people everywhere.

As Joni Mitchell sang all those years ago, something’s lost but something’s gained. Democrats have lost our standard-bearer, and we will miss Joe Biden’s steady leadership, deep empathy and fighting spirit. He is a wise and decent man who served our country well. Yet we have gained much, too: a new champion, an invigorated campaign and a renewed sense of purpose.

• This is an edited extract from the epilogue to the audiobook Something Lost, Something Gained: Reflections on Life, Love, and Liberty by Hillary Rodham Clinton, published by Simon & Schuster. To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.