Quiet at boot

Nothing holds SIGNAL down

SIGNAL goes through 1 kΩ to the transistor's base and nowhere else. Many driver boards add a resistor from the base to GND so an input nobody is driving reads as off. This one does not, so the buzzer's state before your sketch runs is decided entirely by your board: whatever its pin does from power-up until setup() takes it, the buzzer does too.

Pick a pin and power the board up. There are three kinds of answer.

Pulled LOW. A Pico starts every GPIO with a weak pull-down on, so GP15, like the rest, holds SIGNAL low and the buzzer stays quiet from the first instant.

Floating. ESP32-S3 GPIO 4 and an Uno's D9 start as inputs with nothing pulling them either way. A floating pin pushes no current into the base, so the transistor stays off and the buzzer is quiet in practice. Not guaranteed: a long loose wire, or a finger on SIGNAL, can make it click.

Pulled HIGH, or driven. These beep before your sketch has a say.

The pins to avoid

GPIO 0 on an ESP32-S3. On a dev board it carries the BOOT button and a 10 kΩ pull-up. Through that resistor and the block's 1 kΩ it feeds the base about 0.24 mA, which is enough to turn the buzzer fully on, so it sounds from power-up. Worse, the base holds GPIO 0 at about 0.9 V, and GPIO 0 is a strapping pin: the chip reads it at reset and needs a HIGH, at least 2.48 V, to run your firmware. It may start in download mode instead, and then setup() never runs to silence it.

GPIO 43 and 44 on an ESP32-S3. They are UART0, pulled up at reset, and the chip's ROM prints its boot messages on 43. The buzzer sounds from power-up and rasps along with the text.

D13 on an Uno. The bootloader blinks the L LED on D13 as it starts, at every reset and every upload, and the buzzer chirps with it. Harmless, and annoying.

Two lines, first

Whatever pin you use, make these the first two lines of setup():

pinMode(BUZZER_PIN, OUTPUT);
digitalWrite(BUZZER_PIN, LOW);

They shorten any noise to the time the board takes to reach them, which is moments. They cannot fix a pin that stops the board reaching them at all, which is the GPIO 0 case. For that, only a different pin will do.