Should I quit my PhD after 4 months?
No one here should tell you whether to quit or not. But you need to find a changed situation somehow. Some suggestions...
Talk to your supervisor about the situation with your project and see whether there is some alternative that will make things better. Another project? A modification of this one? More assistance?
Talk to others in the research group about how they see the project and its likelihood of success. Are they happy or just coping like yourself?
Talk to a mental health professional about how you can arrange things so that you don't fall into depression. Many universities provide professional counseling.
Talk to your girlfriend about her wishes, goals, and plans. Ask her if she has any advice for you.
Find some &quot;escape&quot; activities so that you don't spend too much time working. My escape was bicycling with a small group. It had the advantage of being aerobic, but other things can help. Resting your mind can actually aid productivity.
Think about your goals as well as whatever options are open to you. Options about staying as well as about leaving. What are the pros and cons of each? How can you achieve your goals and stay sane?
The hardest part, as you describe it, is to find the courage to talk to your supervisors. But that is probably the essential step to find a way out of the dilemma. But don't just continue on, hoping for the best. Some situations need to be escaped.

The biggest mistake I made in my doctoral studies was not speaking up for myself at a certain point. In my case it was because I had an unhelpful advisor. But my lack of courage cost me about three years. I was successful after a change of institutions and only realized later how I'd missed the opportunity. There was also the issue of burnout after an intense undergraduate program.