Do you need the bootloader? If you connect an ISP programmer to your ATmega2560 and do a Sketch > Upload Using Programmer then your uploaded program will overwrite the bootloader. Of course then you can't do uploads via serial.
How "immediately" do you really need to start sending data? I believe the optiboot bootloader has a shorter delay after startup than the standard bootloader used on the Arduino Mega. You can easily install optiboot on your board using this hardware package: