From version 6.1.2 onwards, Sound Scouts has a feature which allows you to skip the adult calibration if you do multiple sessions in a row without closing the app.
This feature will automatically activate on the second playthrough of the game (provided the App remains open). It will simply ask you if you wish to reuse the previous adult data. This screen/option appears after the adult headphone check within the setup stage for a new test.
Keeping in mind that the environment noise (ie any background noise) should be the same.