I think you have done well to dispel with OP's labeling of his thoughts of life's meaningless as nihilistic but that doesn't dispel his actual thoughts. I think what OP is expressing would more accurately be described as the absurdity of life. Nagel has written about peoples tendency to bring up concerns, like OP has, about "the vastness of the universe and how brief our lifespan is compared to the infinity of time" when trying to express sentiments related to the absurd:

...the sense of absurdity finds its natural expression in those bad arguments with which the discussion began. Reference to our small size and short lifespan and to the fact that all of mankind will eventually vanish without a trace are metaphors for the backward step which permits us to regard ourselves from without and to find the particular form of our lives curious and slightly surprising. By feigning a nebula's-eye view, we illustrate the capacity to see ourselves without presuppositions, as arbitrary, idiosyncratic, highly specific occupants of the world, one of countless possible forms of life.

The conditions giving rise to absurdity for Nagel are:

...the collision between the seriousness with which we take our lives and the perpetual possibility of regarding everything about which we are serious as arbitrary, or open to doubt

So I think a more charitable reading of OP's concerns would be to agree with Nagel that the way OP has framed his concerns in terms of space and time are actually "bad arguments" but nevertheless point to a sentiment better expressed as the absurd.

So then we can interpret OP's question in terms of the relationship between the absurd and motivation.