Stoll, who comes from a Swabian pastor's family and grew up near Herrenberg in Kayh from the age of 13, studied geology in Tübingen and Stuttgart and received his doctorate in Tübingen in 1927 for his thesis entitled "Versuch einer stratigraphischen Gliederung des Stubensandstein im westlichen Württemberg".
During this time he devoted himself intensively to the settlement history of the Upper Gäu, where he carried out several excavations in addition to field surveys.
During his time in Tübingen he continued the research begun by Hans Reinerth on the prehistoric hilltop settlement on the Kirchberg near Reusten and excavated the Alamannic cemetery of Hailfingen, which he published in 1939.
In 1939 Stoll began excavations in the Alamannic cemetery of Grimmelshofen, which were continued by Ruprecht Gießler in August after his convocation.
Concessions to nationalist ideas and corresponding terminology, which had prevailed in the Tübingen Institute since the 1920s, are conspicuously rare in Stoll's work.