Is it possible to have no geological (soil and/or wind) erosion at all? why or why not?

No, it is not possible to have erosion at all.

Explanation: Erosion is a natural geological process that has the capability remove the debris of the rocks from the Earth's surface through several erosive agents such as soil, water etc. Being a natural process , it is not possible to not have erosion on Earth's surface. There are certain steps that can be taken to prevent it but cannot completely finish the process.

Erosion occurs in many forms such as soil erosion, water erosion, wind erosion etc.

tropical storm katrina, and it made landfall between miami and fort lauder-dale, florida, as a category 1 hurricane (a storm that, on the saffir-simpson scale, exhibits winds in the range of 74–95 miles per hour [119–154 km per hour]). sustained winds of 70 miles per hour (115 km per hour) lashed the florida peninsula, and rainfall totals of 5 inches (13 cm) were reported in some areas. the storm spent less than eight hours over land. it quickly intensified when it reached the warm waters of the gulf of mexico.

this should answer you're question