ABSTRACT Peter Pan discs are a recently discovered class of long-lived discs around low-mass stars that survive for an order of magnitude longer than typical discs. In this paper, we use disc evolutionary models to determine the required balance between initial conditions and the magnitude of dispersal processes for Peter Pan discs to be primordial. We find that we require low transport (α ∼ 10−4), extremely low external photoevaporation (${\le}10^{-9}\, {\rm M}_{⊙ }\, {\rm yr^{-1}}$), and relatively high disc masses (>0.25M*) to produce discs with ages and accretion rates consistent with Peter Pan discs. Higher transport (α = 10−3) results in disc lifetimes that are too short and even lower transport (α = 10−5) leads to accretion rates smaller than those observed. The required external photoevaporation rates are so low that primordial Peter Pan discs will have formed in rare environments on the periphery of low-mass star-forming regions, or deeply embedded, and as such have never subsequently been exposed to higher amounts of UV radiation. Given that such an external photoevaporation scenario is rare, the required disc parameters and accretion properties may reflect the initial conditions and accretion rates of a much larger fraction of the discs around low-mass stars.