I used to fly AMC airlifters. You are correct airlift is the most flexible, and the fastest. NEOs, depending on the scope, size, and availability of Seaports and Airports - are usually a combination of assets. In 2006, we used commercial aircraft, military aircraft, military ships, and commercial ships. Moreover, the Navy uses the assault groups to provide security during the NEO. From 2006:
Thank you for your service.