Polishing the windshield?

Greetings to everyone Unfortunately, I had to find out that with the windscreen wipers I probably wiped some grain of sand or something about the windshield. It sees two very fine superficial scratches. I now want to try to polish out the scratches myself with a glass polish. Has any of you tried this already and had success? As I said, the scratches are very fine. I have a DA polishing machine from Liquid Elements (T3000) and now also have my own pad for the glass ordered (shinemate felt pad) as well as the Glass Polish by Sonax as well as the Ceriglass by Carpro. Before I reach for the polishing machine, however, I wanted to try it first by hand with an applicator pad. Does anyone have experience with the polish of glass and can you get out such superficial scratches yourself without having to go straight to the workshop? What about the polish by hand? Can I polish out such fine scratches even by hand? Problem to use the polishing machine, but if it also works by hand, I would prefer the method. Thank you for the help.