You did not mention your phone model, so we can only give broad answer:
On my samsung tablet there is easy way without power button. only press Volume Down + Home Button + connect charger will bring up odin mode splash screen (with additional options). with Volume Down select reboot
For more details on how things work please read the linked questions:
How a powered off phone communicate with the power button
What is the fastest way to shutdown unrooted Android phone?
perhaps it is possible to tweak this communication to gain access externally
very hard challenge and not possible by software only, this kind of communication is proprietary low level protocol. furthermore that requires physical access to pcb board
is it possible to turn phone on by using adb or fastboot
No. external access via usb by
adb requires running adb daemon on device. that is only the case in recovery or boot mode
fastboot requires device running on fastboot mode, which is generally not supported on samsung devices
other application on host requires device running in other mode. Such applications are flash tools like Odin/heimdall or EDL programmer tools (qualcomm only)
The auto-reboot after flash trick without power button is similar on most flash tools. It works best on Mediatek devices because preloader mode is activated only by plug in usb cable without pressing any button.
Samsung download mode can be achieved with JIG dongle.
Flashing official stock ROM will reboot phone when done with flashing