Context. The journey from dust particle to planetesimal involves physical processes acting on scales ranging from micrometers (the sticking and restructuring of aggregates) to hundreds of astronomical units (the size of the turbulent protoplanetary nebula). Considering these processes simultaneously is essential when studying planetesimal formation. Aims: The goal of this work is to quantify where and when planetesimal formation can occur as the result of porous coagulation of icy grains and to understand how the process is influenced by the properties of the protoplanetary disk. Methods: We develop a novel, global, semi-analytical model for the evolution of the mass-dominating dust particles in a turbulent protoplanetary disk that takes into account the evolution of the dust surface density while preserving the essential characteristics of the porous coagulation process. This panoptic model is used to study the growth from sub-micron to planetesimal sizes in disks around Sun-like stars. Results: For highly porous ices, unaffected by collisional fragmentation and erosion, rapid growth to planetesimal sizes is possible in a zone stretching out to ~10 AU for massive disks. When porous coagulation is limited by erosive collisions, the formation of planetesimals through direct coagulation is not possible, but the creation of a large population of aggregates with Stokes numbers close to unity might trigger the streaming instability (SI). However, we find that reaching conditions necessary for SI is difficult and limited to dust-rich disks, (very) cold disks, or disks with weak turbulence. Conclusions: Behind the snow-line, porosity-driven aggregation of icy grains results in rapid (~104 yr) formation of planetesimals. If erosive collisions prevent this, SI might be triggered for specific disk conditions. The numerical approach introduced in this work is ideally suited for studying planetesimal formation and pebble delivery simultaneously and will help build a coherent picture of the start of the planet formation process.