iPhone 11 shutdown and won't turn on

Plug in the phone for 30 minutes, next:

• 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. 

Possible results:

1) The phone returns to normal operation.....or if it doesn't.....

2) The phone travels to an authorized Apple service shop

Genius Bar Reservation and Apple Support Options - Apple

3) Or, the phone travels to the recycle center.

it is possible I can just get a replacement iPhone 11

Yes, if you purchase one.