by accident (idiom)

I deleted the file by accident.
I found her letter by accident as I was looking through my files.
She stumbled upon the hidden path by accident while exploring the forest, discovering a secluded clearing she had never seen before.
Without realizing it, he knocked over the vase by accident as he reached for the book on the crowded shelf, causing a moment of surprise and a bit of laughter in the bookstore.
By accident, he took the wrong train and ended up in a charming town he had never planned to visit, turning an unintentional mistake into a delightful adventure.