We are confused over what is “objective” when we assume that there can be answers without questions and a question-asking being – a Dasein, in Heidegger's terms. Dasein comes first and it alone is primordial to our experiences and knowledge. Science is a set of tools for thought and action that depend first and foremost upon Dasein, upon our being in time. There can be no science without thinking beings to conduct it.
Spacetime, then, is a tool that can be at hand for us to use as Dasein (in understanding the nature of the universe as we observe it, for instance) but it does not mean that the concept of spacetime is more fundamental than the notion of time in the context of being and existence. We all too frequently mistake our scientific tools for objective truth because the modern paradigms of science trick us into thinking that our experimental results, and the theories that organise these, are meaningful independent of humanity. But this is far from the case: they are a product of our being, our Dasein. Another kind of being would not necessarily derive the same theories.