System Data fills new 1TB MacBook Pro in a Month

Download and run this app so we can find more information about your installation. It appears you have an app that is generating a lot of the "System Data"

https://etrecheck.com/upgrade

It shows what is launched and other information and is very useful in finding causes of problems. After you first launch the app make sure you check Enable full disk access in the box in lower left.

After running the app use the app's feature to paste to clipboard. The in the text box for a reply in this forum click on the addition text icon. This is because the normal reply text box limits how much you can type.

o personal identifiable information is contained if the app output. The app was written for a person who is contributor to these Apple Support Communities

Edited - if this situation is left not correct fast the computer may Stop booting at ALL

Then one would have to explore Transfer files between two Mac computers using target disk mode

Manage Storage

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

How to delete Time Machine snapshots on your Mac

See used and available storage space on your Mac

The final word from Apple on Managing the " Other " Category

Other: 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.

I definitely concur that you need to immediately make a backup while you can since you may lose access to the files stored on the laptop because it may be impossible to mount a drive with no free storage space. If you value your data, then you definitely need to start backing up your computer. Get the data off before rebooting the Mac. You may need to first delete some unimportant files to make a bit more room and don't forget to empty the Trash.

You should always have frequent and regular backups of your computer and any external media which contains important and unique data. FYI, it is impossible to recover accidentally deleted data from an SSD after the Trash has been emptied. Plus if the laptop ever has a Logic Board failure, then it is most likely impossible to recover any data from the laptop due to the data being hardware encrypted even by an expensive professional data recovery service.