accidently clicked "don't save" on my word doc

I was restarting my computer for a update and had not saved my doc, it asked me if I wanted to save it and I miss clicked and hit “don’t save”.

I want to recover that doc if possible. I wonder if it is possible?

No. Once you click “Don’t save” the data is not saved. There may be data recovery solutions which can recover deleted auto-save data, but these are outside of the scope of LibreOffice.