Miniature Lepin box door stuck inside box itself
Finally, I did it. I wasted two days waiting for answers when the solution is actually very simple.
I just lifted the box cover with my fingertips just a tiny bit, so that there was enough space to stick something thin between the box cover and the box itself. I did not lift as much as possible because:

My fingers would slip and drop the box lid again, because the remaining space to lift it all the way out would be too tight

I need enough space to stick something thin in between.


Then I got a thin-blade knife, as zovits recommended, and pulled it down like a lever, making the other end go up and force the cover out. Easy!