There is no way to be sure in practice. You just can make reasonable assumptions. If the sum of all forces is not zero you have to decide weather you describe the situation with unknown interactions or with a non-inertial system (or both).So in practical case how can we be sure if a frame is inertial or non-inertial?
The first law is neither necessary nor sufficient for the identification of inertial systems. The second and the third law can do the job if you know all interactions.Also it seems like Newton's first law is not enough to check for an Inertial frame.