leveling the bed with a paper

Hello!

I have an Ender 3 and have a hard time leveling the bed. The problem is that I have to go with the nozzle very far down to the bed that I have a hard time getting a thin paper between bed and nozzle. But only then I get a good first layer where the lines stick together.

Since this is my first 3D printer I don't know if this is normal but I doubt it. I have seen calibration videos where people can easily fit a paper under the nozzle or even use a business card for this. I would say my nozzle is even touching the bed already. If I've, however, a small gap between nozzle and bed my lines are separate.

Is it possible that the nozzle is damaged so there is not enough filament coming out or can there be a another reason for this?