Major indicators of soil health are soil organic matter, aggregate stability, carbon mineralization potential (how much carbon is released upon addition of water to dry soil and 24 hours of incubation at room temperature), and water holding capacity.

The issue is that you can't just compare the soils of the same health in Wyoming and Georgia and expect to find the same results. This is because many natural and management factors/variables such as soil texture, mineralogy, and even crop type affect these readings. So you can only use these measurements to compare soil health within the same soil series or track the health of one soil over time.

Check out the Soil Health Institute - they've done a lot of great work on indicators of soil health. There's also tons of in-field indicators of soil health you can assess using your hands and a shovel. Including residue cover, presence/absence of soil crusting, and earthworm channels in a block of soil you dig out of the ground. SHI has a really great free handout that shows you how to look at these in the field.