Foundation design is critical. The deck is suspended from the main large cable by smaller cables. The record span for a suspension bridge is 4600 feet. A newer design called a cable stayed bridge is like a suspension bridge, but cables which hold the deck are placed at angles from the main towers. This type of bridge is very stable in wind and earthquake loads.
Steel is strong in tension, concrete is strong in compression.
Wood is easy to build but not as strong or durable as steel and concrete. A highway overpass can use the ground for people and supports to hold the bridge . Pouring concrete and letting it cure will be fine. A deep mountain gorge, or a river may not have anyplace that allows work from below. In water we may be able to drive piles to help us get started.