It feels to me like there must be more than just you're born and then you die.
Yes, your entire life in between. Life is a palet and we can paint, draw, construct, OR destroy in any way we choose. This might sound schamltzy, but it's reasonably true.
The extreme example in support of what you suggest is the monk who spends his entire life in the pursuit of what's behind the "more than just you're born and then you die". The irony is that for this monk there has been "just" being born and dying and no reason for living beyond himself. That is truly the epitome of no reason or purpose for one's life....you've done nothing with it.