How do I overcome nihilism

Find meaning

You don't. You accept that life does not have an inherent meaning or purpose and the implications that follow. One of them is that you can define meaning and goals yourself. As the typical human brain really likes meaning and purpose, i recommend actually doing so.

you don't.

you revel in your accomplishment of seeing the world for what it is.

Quantum mechanics need you.
Just keep looking at stuff.

Thats it. It is that simple. Or really really really complicated.

You find meaning, or you accept you are nothing but an accidental spec of dust amongst the cosmo's

More importantly, _why should I_ overcome nihilism

You find the futility in futility :)

Then the paradox shows how absolute meaninglessness means something, that you can define your own meaning and make what you want.

In my experience, acceptance of it.