I'm wondering... If the Earth didn't have a magnetic field for a while, how deep would a submersible need to be to be protected?

According to this article, there was a period of 400 years, 42k yrs ago, with basically no magnetic field, and it caused people to start living in caves.

https://www.npr.org/2021/02/18/969063568/ancient-trees-show-when-the-earths-magnetic-field-last-flipped-out