how did the people went from nomadic small groups, to one of large populations and eventually civilizations

Human groups became larger as they acquired new sources of foods. These new sources of foods allowed them to be able to support larger populations.

From hunter-gatherers, they became pastoralists, and from pastoralists, human gruops became farmers, when they learned how to practice agriculture.

Agriculture produced food surpluses, which led to the development of even larger human groups, and finally, civilizations.