Over time the calluses on your finger will get harder. It has the effect of not only making it firmer when you press down the note but also reducing the pain. It really is just part of a process.
There’s another thing going on. You’re making subtle adjustments on how you angle your fingers and where you place them on the fretboard. It’s not something you usually get just right in the first few weeks… Or even months.
Pressing harder is not the only way to reduce the buzzing. But it usually takes a while to figure out the subtle movements.