Is fast charging a Lithium-Ion battery from 0% to 30% better or worse for the battery health than fast charging at 30% to 70%?
This BU article indicates that recommended method is to fast charge from 0% to (in the case illustrated by the 2nd graph) about 60%.  This is a typical charging cycle.

However, Li chemistries can be overdischarged by continuing to draw current after reaching the "dead battery" threshold.  Many have protective circuitry that prevents charging if overdischarged (since self-discharge is one common source of overdischarge).  Some of these cells may recover if trickle charged to 2.5-3V, after which they can accept full charging current.