The fine structure of a streamer–to–filament transition in a single–shot high–voltage nanosecond surface dielectric barrier discharge (nSDBD) in molecular nitrogen at pressure $P = 6$~bar was studied with the help of ICCD microimaging. An intermediate discharge structure, existing for only a few nanoseconds, was observed in the time interval between two discharge modes: streamer discharge, with a typical electron density of $n_e \sim 10^{15}$~cm$^{-3}$, and filamentary discharge, with $n_e \sim 10^{19}$~cm$^{-3}$. The structure was observed for both polarities of the high–voltage electrode. The structure can be briefly described as a stochastic appearance of thin channels propagating a bit faster than the main ionization front of merged surface streamers, transforming in a few nanoseconds in a bi–directional ionization wave. One wave, which we associate with a feather–like structure in optical emission, propagates further away from the high–voltage electrode, and another, a backward wave of emission, propagates back towards the edge of the high–voltage electrode. When the backward wave of emission almost reaches the high–voltage electrode, the filament appears. Plasma properties of the observed structure were studied to better understand the nature of a streamer–to–filament transition. Theoretical analysis suggests that the instability of a flat front of ionization wave (Laplacian instability) triggers the streamer–to–filament transition, and that a surface stem (a tiny region with enhanced electron density) should be in the origin of the bi-directional ionization wave.