I think the notion of rights is a consequence of our being creatures with free will, i.e. the faculty to discover what is good, and to choose to do it. Since each of us was created with that faculty, it would in defiance of the Creator to thwart it.
I suppose when this country’s founders spoke of self-evident truths, that’s what they were referring to.
So the “liberty” is the guaranteed right to exercise free will.
I guess my line of argument boils the right to life and liberty down to the genetic possibility of being able to exercise that free will if and when you make it out of the womb.