As above, FTTP generally comes from an exchange or data centre headend. However, there are such things as mini-headends or mini-OLT (Optical Line Terminals) - also known as a subtended head end, which can sometimes be installed alongside or inside existing cabinets (FTTC / VDSL2 or PCP). Openreach may deploy these in certain rural areas.
I've also seen some other operators that build very large cabinets that effectively act as mini exchanges for rural FTTP deployments. You won't see these on street corners though as they're too big, so they'll often be hidden away on a private site somewhere. In other words, FTTP comes from an exchange, but how you define an exchange is another matter.