When you first apply power - before your microcontroller can do anything - the power you apply charges up all the power-supply-decoupling capacitors in your system.
The handful of 0.1uF high-frequency decoupling capacitors are probably not the issue here.
More likely if you have 10uF to 100uF of electrolytic (or more) before or after the 3.3V regulator, they will contribute a huge amount to the inrush current, possibly enough to trip your overcurrent detector.
What stm32 microcontroller are you using? Many would not burn as much as 100 mA when running flat-out, so there's little you can do to fix things there.
It would be handy to measure the current - put a small (say 1 Ohm) resistor in series with the power line to your mcu board and measure both before and after the resistor with an oscilloscope. Is the highest current in the first millisecond or two of applying power, or does it happen (say) 10 - 100 ms later? If the latter, it could indicate that it is the mcu software startup, but do show us the results.
Another issue - does your mcu switch / drive high currents? Until it has started running your code, the GPIO outputs will be high-impedance. Do you have resistors to ensure any driver switches are turned off during the time the processor is in reset?
Finally I will add that until you have first programmed the stm32, it will start up in ST's bootloader. This drives certain pins as e.g. UART, I2C; see AN2606 STM32 microcontroller system memory boot mode for which pins are driven and how. This may also cause high currents depending how you use those pins.
