How to fault find MacBook Pro that shuts down very soon after boot?
Sounds like your hardware is fine and you have a brand new SSD.

Steps to heal it.


You can double check your hardware using the Apple Hardware check.

Press D during startup (for Hardware test) you might no longer have it on your hard drive so do not worry for now)
Disconnect all external devices to make sure they do not do something stupid.
Start in Safe mode to eliminate other programs interfering.

Press Shift during startup


If you mange to start open Console and look for logs before this start, and for reason why it shut down.


If the safe mode fails then try the Start up in Verbose mode.

Press Command-V during startup  


This is line by line mode showing you each step. Sometimes it will show your where it got hung up.

In any case your best source of information is the Console (but it requires a running computer)