As I keep saying, you have a four-dimensional manifold (object) that contains time as one of the directions though it. I don't get why you find this so difficult.
Perhaps if you imagine that the surface of the earth represents space-time, with two of the three spacial dimensions suppressed, so (say) north-south represents time, with (say) north as the future, and east-west represents space. Then if we follow time, we start at the south pole (the BB), where space has zero size, then go north, and see that space expands until the equator. In this toy universe, space would then contract again into a 'big crunch' at the north pole (we we don't think is likely for the real universe). Anyway, in this picture, time is a direction on the surface of the earth, so the earth itself simply wouldn't experience time.