Whether asphalt pavements would hold up structurally, is mostly dependent on what the rock, that it is made of. In many types of stone, water will make the asphalt binder let loose of the rock, pavement engineers refer to it as stripping.
A single layer of concrete in large slabs might, big might, work. The doublelayer over lapped lik brick would work a bit better.
But both asphalt and concrete pavements in the 4 to 6-inch thicknesses are referred to as “flexible” pavements in roadway design. Your best bet is to place some 2-inch minus, 3/4-inch plus crushed aggregate, (reject coarse concrete aggregate will be least expensive, if you can find it), with a lot of fractured faces. Spread it out, then drive over it to sink it into the mud, and keep doing it until the rock starts to bridge, and bring it up to a bit bone the level you want the road. If it settles in the future add more stone.
You do not want to add what is referred to as a road base or Type-II, or Type 87, all of them have fine material in them, and because your road is muddy, you a lot o fine material and not enough coarse material to have strength when wet. Adding larger, angular material will help stabilize the soil.