The occurrence of stripe domains in ferromagnetic permalloy (Py = Fe20Ni80) is a well-known phenomenon which has been extensively observed and characterized. This peculiar magnetic configuration appears only in films with a thickness above a critical value (dcr), which is strongly determined by the sputtering conditions (i.e., deposition rate, temperature, magnetic field). So far, dcr has usually been presented as the boundary between the homogeneous (H) and stripe-domain (SD) regime, respectively, below and above dcr. In this work we study the transition from the H to the SD regime in thin films and microstructured bridges of Py with different thicknesses. We find there is an intermediate regime, over a quite significant thickness range below dcr, which is signaled in confined structures by a quickly changing domain-wall configuration and by a broadening of the magnetoresistance dip at the coercive field. We call this the emerging stripe-domain (ESD) regime. The transition from the ESD to the SD regime is accompanied by a sharp increase of the magnetoresistance ratio at the thickness where stripes appear in MFM.