The NUC is designed to boot and work without monitor attached (also keyboard and mouse need not to be attached). See para. 3.7.2 in Product Technical Spec.: https://www.intel.com/content/dam/support/us/en/documents/boardsandkits/NUC6i7KYK_TechProdSpec.pdf
What happens with your NUC after Power Button is depressed, depends on system settings. In my NUC (with Windows 10 Pro), after short depressing, the NUC shuts OFF. You can verify that your NUC is working after booting without monitor. Just connect a monitor after some time and you will see that it is working.