It's not a requirement. It's just ceremonial. They could put their hand on top of Mein Kampf if they wanted to.
(quick from AI) George Washington: Started the tradition of using a Bible for the presidential oath. Theodore Roosevelt: Took the oath of office without a Bible after William McKinley's assassination. John Quincy Adams: Placed his hand on a law book during his inauguration. Lyndon B. Johnson: Took the oath on a Catholic missal following John F. Kennedy's assassination.
On a more simple side, I'd like to know how shitstain was the first president since Washington to not put his hand on the bible while being sworn in, and how he was allowed to do so.
No one has to be sworn in on the Bible. We are NOT a religious state.
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
Article 6, Section 3 of the United States Constitution
As you'll see in the article cited, there's been quite a lot of variety in politicians' choices. Robert Garcia--often seen on TV these days for his opposition to Trump--used a rare Superman comic:
Congressman Robert Garcia was sworn in this past January to serve as a California state representative of the 42nd congressional district, and one of the items he chose to swear his oath of office on was a beloved and rare Superman comic. Garcia used comics to learn to read and write in English as a child after he came to the United States from Peru, and he chose Superman because he embodies all of the values that Garcia wishes to uphold — and also happens to be an immigrant.
He borrowed the comic from the Library of Congress for the occasion, and was also sworn in with a copy of the Constitution, his citizenship certificate, and a photograph of his parents, both of whom died of COVID-19 in 2020.
And there's a woman--not a national politician--who used a Dr Seuss book as a tribute to her children, who held it up for her.
A woman serving as an ambassador chose to use a Kindle, which I think is clever.
As for Trump, he took two bibles to both of his inaugurations. He just forgot to put his hand on them at the second one. That's what you're thinking of. But he didn't have to bring anything with him at all: