  Models of dust coagulation and subsequent planetesimal formation are usually
computed on the backdrop of an already fully formed protoplanetary disk model.
At the same time, observational studies suggest that planetesimal formation
should start early, possibly even before the protoplanetary disk is fully
formed. In this paper, we investigate under which conditions planetesimals
already form during the disk buildup stage, in which gas and dust fall onto the
disk from its parent molecular cloud. We couple our earlier planetesimal
formation model at the water snow line to a simple model of disk formation and
evolution. We find that under most conditions planetesimals only form after the
buildup stage when the disk becomes less massive and less hot. However, there
are parameters for which planetesimals already form during the disk buildup.
This occurs when the viscosity driving the disk evolution is intermediate
($\alpha_v \sim 10^{-3}-10^{-2}$) while the turbulent mixing of the dust is
reduced compared to that ($\alpha_t \le 0.03 \cdot \alpha_v$), and with the
assumption that water vapor is vertically well-mixed with the gas. Such
$\alpha_t \ll \alpha_v$ scenario could be expected for layered accretion, where
the gas flow is mostly driven by the active surface layers, while the midplane
layers, where most of the dust resides, are quiescent.
