Can I use a low dropout voltage regulator to drop a 5V 100 nSec pulse to 3.3V?
A regulator is not a good option. Too slow and possibly not stable without capacitors.

You could use a resistive divider, but another option is to use a purpose-designed level translator chip such as the 74LVC1T45, which can work from 1.65V to 5.5V in either direction. When converting 5V to 3.3 it has a propagation delay of less than 5.4ns over the whole temperature range. It also draws hardly any current normally when not switching.