I've got the same issue.
I'm a remote developer and my company sent to me a new machine.
Just unpackaged fresh MacBook Pro 16 (model a2141, MVVL2RU/A, 2.6GHz 6C / 16GB,AMD Radeon Pro 5300M 4GB / 512GB).
It wasn't charged which is strange for Apple product - usually you expect it to turn on right out of the box.
And now it was trying to charge for almost 24h but it still won't launch.
I can see keyboard lit and battery icon on screen for about 10 sec and then it's turning off.
I've checked that wire and adaptor are working, because they were able to charge another MacBook Pro 16 but with a little different configuration (A1990)
Soo look's like I need to get replacement...

UPDATE:
(Excuse me for my English...)
Okay, so, after a day of searching for a solution MacBook finally turned on.
What I did?
Actually I do not have any special solution for this, I can only explain what were the trials.
I tried to reset SMC many times randomly using different schemes from internet, because they are differ for MacBook generations. Every scheme was tried more than once, so I'm not sure that it was a solution.
Before that I tried to charge MacBook using every usb-c port without any luck. But MacBook even didn’t become warm.
So what I noticed:
If you plug usb-c wire you can see battery icon with and little thunder icon for about 10 secs. If you unplug the wire screen will turn off immediately.
So I tried to check every port successively. I plug a wire, see icon and then unplug it so screen become black.
I tried this for every port several times and on the next trial I saw that little thunder icon changed for a millisecond before screen turned off.
It was something new and after that I plugged wire in again and noticed that MacBook become warm. After 15 minutes I tried to unplug and plug wire again and MacBook turned on.
I do not now if it was any coincidence or whatnot but this is what I did.