New iPhone 16 won't turn on

First, try a forced restart:

Charge the phone for at least 15 minutes, then:

• Press and quickly release VOLUME UP

     then

• Press and quickly release VOLUME DOWN

     then

• Hold the SIDE button until an Apple logo appears (15-30 seconds), ignoring "slide to power off" if it appears

The operative word here is QUICKLY; and try it a couple of times, the timing is a little tricky. If done correctly this will always work unless the phone has a hardware problem. 

If that doesn’t fix it, take it back to the store. Was this an Apple store, BTW?