I haven’t read much Nietzsche and I didn’t hear that RadioLab either, full disclosure. But what I see going on is you looking at life from the outside and noting that it is meaningless. In that view, yes, it is meaningless. The only meaning life is going to have is what you give to it. You have to put yourself inside it, own it, and give it a meaning.
Sure, you could let other people give it meaning for you. Join a religion- they’ve got it all prepackaged and waiting for you. If you can stick to the script and stay with the program, they’ll probably take you in and at the least you will get some casserole out of it. Doesn’t a casserole with some religious fundamentalists sound nice?
But that doesn’t sound like your cup of tea. So you have to go the give-it-meaning route. You will have to affirm yourself as the giver of this meaning, you have to see yourself as somebody even if you are not influential, because at the very least you have this power to assign a meaning to your life. It is actually pretty cool, so use it.
But what? Maybe start small. Think of a jungle wildcat- it doesn’t ask these questions. When it gets hungry, it hunts down something and eats it. That is the meaning for that time. When it gets tired, it sleeps and that is the meaning. When it gets horny, it goes and screws another wildcat, and that is the meaning. Things aren’t very complicated for an animal. We are pretty much animals ourselves, so maybe give a go at enjoying being an animal. 4 billion years of evolution isn’t all wrong, it is actually pretty cool if maybe a little gross sometimes. This way of looking at things may not cheer you up if you are especially sick or weak or something, but even then, c’mon, it is still pretty cool, admit it.
But apparently being just an animal isn’t good enough for evolution. No, we have to be self-aware and capable of language, abstraction, imagination and so on. We can use those things, or we can neglect them. But why neglect them? The jungle cat is free from philosophical questions at the price of having only a few modes of existence. We are able to torture ourselves with questions, but we have far more modes of existence relative to animals (Btw, one of them is ethics. We can assign the value ‘bad’ to some things, then focus exclusively on those things, then get really sad. If you can assign the value ‘bad’ to things and get sad, you can assign meaning to your life, too.). Use your uniquely human attributes rather than neglecting them. Use them to create a meaning for your life.
And don’t give up. That’s the main thing. Die with your boots on if it comes down to that. Then people will say, “Well, at least he died with his boots on, an example to us all.” In that case, you wouldn’t know that meaning of your life until it was over.