Cell shape affects proliferation and differentiation, which are processes known to depend on integrin-based focal adhesion (FA) signaling. Because shape results from force balance and FAs are mechanosensitive complexes transmitting tension from the cell structure to its mechanical environment, we investigated the interplay between 3D cell shape, traction forces generated through the cell body, and FA growth during early spreading. Combining measurements of cell-scale normal traction forces with FA monitoring, we show that the cell body contact angle controls the onset of force generation and, subsequently, the initiation of FA growth at the leading edge of the lamella. This suggests that, when the cell body switches from convex to concave, tension in the apical cortex is transmitted to the lamella where force-sensitive FAs start to grow. Along this line, increasing the stiffness resisting cell body contraction led to a decrease of the lag time between force generation and FA growth, indicating mechanical continuity of the cell structure and force transmission from the cell body to the leading edge. Remarkably, the overall normal force per unit area of FA increased with stiffness, and its values were similar to those reported for local tangential forces acting on individual FAs. These results reveal how the 3D cell shape feeds back on its internal organization and how it may control cell fate through FA-based signaling.