How to make the player start with fists only?

STRAIN is vanilla and gives the player no starting ammo which is the equivalent of a fist start, so try checking out its dehacked script.

If mapping in UDMF format you can do it via script.

#include "zcommon.acs"

script 1 enter             //FIST ONLY START
{
    ClearInventory();
    GiveInventory("Fist", 1);
}

So is there no way to script it in Doom 2 format?

Thanks!

The only thing you need to add is a dehacked file with the following code:

Misc 0
Initial Bullets = 0