The PS4’s power-on sequence is not like a PC. The console uses the 3.3V standby rail to keep the Southbridge (SORI/Renesas chip) alive. When you press the power button, the Southbridge sends a PS_ON signal to the original PSU. On a PC PSU, we must replicate this.
Here are a few links to guides and forums that might be useful: adaptar fuente de pc a ps4 fat
Beep.
Solder / crimp to female connector: