The requirements for substitute teaching vary significantly by state and even by school district within a state. While some states might allow you to substitute teach after completing two years of college, many others will require a bachelor's degree or at least a certain number of college credits. Some might also require you to be enrolled in a teacher training program.
In short: No, you can't assume you can substitute teach after two years of college. You need to check the specific requirements of the state and school districts where you want to work. Contact your local school district's human resources department or the state department of education to find out their exact requirements.