Sometimes my nozzle drags on the first print when I haven't calibrated the Z-height well enough, however, I just designed and printed a much better Z-height calibration piece and now it's very stable and I don't have that problem anymore. So it could be your Z-height of the first layer isn't correct and then the printer outputs too much plastic and after that, on the second layer, it will hit and scrape the first layer because the printer *thinks* it goes up for example a 0.3mm while in reality it is less because the nozzle was too close to the printbed to start with.
For me the range of problems in my printer would be in order of importance:
1. Extruder and hotend calibration (this is the 'heart', the most important part)
2. First-layer Z-height calibration (this is the 'ground', the base of your prints)
3. Print temperature calibration (this is the 'blood' that the 'heart' pumps around)
4. Heatbed temperature calibration (this is the base for the 'ground', if it's bad you print on dust and it falls off, if it is good you print on concrete and it sticks like mad)
5. Print speed calibration (this is your 'heartbeat', too fast and you pass out, too slow and you pass out, too fast, your prints will lose shape, motors will lose steps etc, too slow and your prints might come out saggy and deformed, however, too slow is less worse than too fast)
6. Bridging calibration (this is just an extra, but when your printer bridges correctly, it is much more of a breeze to print objects without support, because if you can bridge well, support structures aren't always needed. Good bridging also helps printing items with overhang. If your nozzle is not pointing straight down, your overhang might stick to the nozzle too, so make sure everything is square)
I hope that helps. And if anyone disagrees, just add/change to whatever you think is more important
I might have forgotten stuff.