The following is based purely on the small amount of information in your question. You haven't described your code or your setup, which would allow this answer to be more specific.
According to the FireBeetle ESP32 schematics here, you should be able to connect an external power supply between VCC(+) and GND(-).
The voltage regulator on the FireBeetle ESP32 is a low-dropout RT9080 regulator, which, according to its datasheet has a maximum voltage drop of about 0.5 V when outputting the 3.3 V needed by your board and a maximum input voltage of 5.5 V.
That means the voltage supplied at VCC should be between 3.8 V and 5.5 V, and the ~4.5 V supplied by your 3 x AA batteries (assuming they're connected in series), falls nicely into this range.
The fact that your board does not seem to run your code might be caused by a number of things.
- Does your program expect a Serial port connection which, of course, is not available when it's not connected to a PC by USB?
- The power demanded by your board might be too high for the batteries. Are there other things connected to the board that that could cause that?
If you have a multimeter, you should be able to measure a stable 3.3 V on the 3.3 V pin of the FireBeetle.