"Just keep writing. Your perfect beginning is probably right ahead of you."
Johanna Harness (writer of YA fiction)
I very often use the very first line I type into the blank document, but rework the other lines on the front page until the mix is just right. I've never dropped the whole first chapter or any substantial chunk of writing. Jumping into the middle of the action helps avoid the need to lop off the beginning. The "action" does not have to be a high-speed car chase. The action is more likely to be an embodiment of the main character's normal life.
I know many authors who write in speed mode to get thoughts on paper. They feel that the pages they discard were valuable in getting into their characters' heads, the scene, and the tone of the book.