When the mcu resets, it wants the pins to be in a safe state. This means "don't drive anything" (as configure it to be an output), and "stabilize the line" (don't leave the line floating). Convention says use a pull up (versus a pull down) and make it strong enough to stabilize the line, but not so strong that it it is difficult to overrule with with a different source. Because of this, industry typically settles on a weak pull-up value of 10kOhms.
If you want to "win", you'll 1) be needing to go the opposite direction (so adding a pull-down) and 2) select a value that will put the outside device in the right state.
One extreme is choosing to short the output directly to ground. That will guarantee that when your mcu starts up the output will be 0 V. That's not very practical because then you can't override the direct short with the mcu because it doesn't have amps of current available.
If you choose a 10kOhm pull down, for example, and your output it is 3.3 V, then the device that you're driving with it in power up will see 3.3÷2=1.65V. Keep in mind that your transistor will require a tiny amount of of current so the voltage at this point might vary a little bit.
So how much of a pull down do you need? As noted above, 1k is much smaller than 10k, so it will likely win the competition and you'd end up with 3.3(1k/(1k+10k))=0.3V. The drawback is that when the mcu drives 3.3V directly to the node, it will have to drive that pull down too, resulting in 3.3/1k= 3.3mA of essentially wasted current. Of course, if you're MCU is plugged into the wall then this is a little concerned; however, if it's powered by a button cell battery then 3.3mA of current could be is considerable drain on it.
So in search for the optimal value of the pulldown resister that will allow you to win the competition on reset, the most important thing to consider is what you're driving. You'll need to find out what the minimum input voltage is that will allow it to be in the correct state, and then, using the voltage divider equation, figure out what the pulldown resistor's optimal value is (and then make it a pinch smaller to guarantee operation over your environment parameter variables, such as temperature.