How to jump the first gap in E4M2, Perfect Hatred:

Remember that in classic Doom games you can Run as well as
Walk. In original commercial PC Doom games the default Run
button is the Shift key.  Hold it down while moving in any
direction to increase your basic movement speed.
In modern console versions of classic Doom/Ultimate Doom,
Run is usually assigned to a Left Trigger.  In early PS1
Ultimate Doom, Run is the Square button by default.

Simply back up a few paces, and Run forward to "jump" across
the gap.  You can also try "strafe running", a simultaneous
combination of Run-forward plus Strafe-sideways.  This moves
the player character at an odd angle, but at a speed which
is slightly above that of plain Running.