Unexpected shutdown while turning on the mac

Namaste, khush raho 🇨🇦

This looks like a Lack Of Empty Space on the Internal Drive.

The fact the computer will start after a shutdown and left that way for " 3 - 4 hours " is a good indicator

Shutdown and Restart immediately does not get the the computer time to clear some caches files

The 3 - 4 hours Off and startup may have given the machine enough time to clear just enough Space on the drive to allow it to startup.

It is generally a good computer practice to alway keep at least 15% to 20% of the Total Drive Capacity’s as Empty Space.

Allowing the computer to drop below these guidelines may eventually, cause unintended consequences including what the computer is experiencing now.

There is Purgeable Space and there is Empty Space.

Purgeable Space which is Controlled by the Operating System. When the Operating Systems decides the computer needs additional Empty Space, it will move a portion of the Purgeable to Empty space

AFAIK - there is no User Actions to hasten this transition from Purgeable to Empty Space

It can day or longer before this will occur  

The links below will assist in identifying what is taking up space on the Internal Drive and provide possible ways to remove data that is under the direct control of the User ( Home Folder ) . 

Rebuild the Spotlight index on your Mac

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

OmniDiskSweeper Safe to use

GrandPerspective 

How to delete Time Machine snapshots on your Mac.  

Often caused if the Time Machine Drive has not been attached  to the computer and TM Backup is set to run on a Schedule. 

TM Backup will make Snap Shot on the Internal Drive awaiting the TM Backup Drive to be attached. 

Only then will the Snaps Shots be transferred to the External Drive and deleted the Internal Drive.

See used and available storage space on your Mac

Locate backups of your iPhone, iPad, and iPod touch

Notation - If the user is using a cloning software like Carbon Copy Cloner - and https://bombich.com/kb/ccc6/automated-maintenance-ccc-safetynet-folder suggest tweaking the Safety Net Feature in this software. It may be making additional Snap Shots that are not being Cloned to the Eternal Drive. If this should be the case, these Snap Shot could be using additional space on the drive 

The final word from Apple on Managing the " Other/ System Data “ Category

Other / System Data: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

" When I power it on again, it does the same and many times it would shut down even before the login window appears. If I give my mac a rest of around 3 - 4 hours, it starts normally. But if I shut it down and restart, it would still have the same startup problem. "

At this point the issue could be Over Heating, Lack of Empty Space, or some other Hardware issue

Then have a few suggestions ;

1 - Have the computer evaluated by the Professionals who have the Special Hardware Software and Expertise to diagnose the issue and offer possible solutions

2 - Make an Appointment at the Apple Genius Bar and have them evaluate the computer