I'm pretty sure there's an option in BIOS that lets you use the keyboard to turn the NUC on. 99% sure.
You can also wake from network access within BIOS.
Third option is that there are internal headers from which you can extend a wire which you use to turn the NUC on and off with. That way you can still have a physical button if you have the NUC hidden somewhere.
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Thank you very much to jbabels for the information provided previously.
carmor, Thank you very much for joining the Intel® NUC communities.
To answer your question, if the NUC is off, in order to turn it on externally you can try the CIR feature with a remote control, or as it was mentioned previously, you can always use the internal headers of the NUC to extend a wire for power.
There is no an option in the BIOS that allows you to turn the NUC on with a keyboard. In regard to the wake on LAN option, it will work only to wake the NUC from soft off or S5 state, it will not work if the NUC is completely off.
Any further questions, please let me know.