The notion of curvature in Earth's sense is applicable to its surface. No one is expecting to find oneself at the starting point having dug through the innards

The notion of curvature in Earth's sense is applicable to its surface. No one is expecting to find oneself at the starting point having dug through the innards of our precious home. Why would we consider such a premise in the case of the Universe, when we are clearly not aware of any facts proving an existence of its surface? At best we're inside the Universe. Moreover, how would one define the 'sameness' of the final point? Is it in relation to neighboring objects or to some static reference point? How one could even ascertain the static property of such a point?