On a keyboard, play C, E and G together in a comfortable register. Now try E, G and the next C above them. The same three note names are present, but their arrangement has changed.
Follow the lowest note
For this C-major example, C at the bottom gives root position. E at the bottom gives first inversion; G at the bottom gives second inversion. Move gently between these arrangements and listen for the changing bass position rather than simply calling the second version a different chord.
Keep the exercise small
Use a manageable volume and avoid stretching your hand uncomfortably. You can play the notes slowly in sequence to find them before sounding them together. Do not add extra notes until the comparison is clear.
Write the bottom note beside each arrangement. Then listen to a short progression and ask whether a smooth bass movement interests you more than the individual chord labels. This exercise introduces one organising idea; identifying every inversion in a dense recording is a much harder task and is not required to hear the basic contrast.