Powering ESP32 from Battery with Power Supply Module

[Flammlachs]

Hello!
Couldn't find the right answer to this anywhere, so lets try here.

I'm trying to get my ESP32 to work powered by battery. I want to use a power supply module which gets power from a 9V battery.
The power supply module gives 5V to the esp32, which should be enough.

Why does the code not start when the ESP32 is powered like that?
I have a project which controls two LEDs from a webserver setup by the ESP32. That works fine if the ESP32 is connected to the computer with USB.

Thank you for your help and I'm sorry if this is a dumb question, fairly new to all of this.

[ESP_Sprite]

What exactly is this 'power supply module'? In general, 9V batteries can't always deliver the power the ESP32 needs as they tend to have a fairly high internal resistance.

[JoeSensoric]

I'm using a Pololu 3.3V, 500mA Step-Down Voltage Regulator D24V5F3 to power my ESP32 board with four AAA batteries. The ESP32 runs with 3.3 volts, the 5 volts coming from USB are regulated.
The batteries and the regulator need to able to handle the spikes when the WLAN is activated.
As asked above: What kind is your "power supply module"?