I don't want to ask about potential resolutions to the arrow of time. On the contrary, I want to take it as a given that it is the case for the universe, but then ask a rather odd question about its applicability (or lack thereof) to the surface of the earth.
The surface of the earth is certainly not a closed system, in that it receives tremendous energy from the sun. For that reason alone, there is no reason to believe its entropy should increase over time. Shouldn't I be able to conclude that, for processes that are only sensitive to conditions on the surface of the earth, there is no arrow of time ? Shouldn't be this be the case for life as a whole ? If I were studying large scale structure formation in the universe, it would make sense to keep in mind that there will be an asymmetry in the change in entropy between one direction and another given the low entropy of the initial conditions. The evolution of life clearly also follows this asymmetry in that if I were to ask in what direction of time I would have to go to find the common ancestor of 2 animals, it would be the same as the low entropy direction of the universe, but there's no clear reason why that should be the case (in other words, if I were to reconstruct the tree of life, there would be a direction from which branches can flow out of points, but never into them). The bacteria floating around a puddle of water are hardly sensitive to the entropy conditions of the whole universe, and only care about their immediate surroundings. More generally, as I've pointed out, there is no reason to think that the surface of the earth will have greater entropy in a billion years. So why can't life appear in the future, and evolve "backwards" relative to us, leading to a separate time reversed tree of life from us ? Why isn't there a second tree of life that sees time "backwards" relative to us, with living beings that seem to multiply "backwards" in time ?
More generally, if this cannot be the case for the surface of the earth if the energy from the sun simply isn't enough to accomplish it, can there exist local systems whose arrow of time will be the opposite of the global arrow of time ?