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Aims. The initial stages of planet formation may start concurrently with theformation of a gas-dust protoplanetary disk. This makes the study of theearliest stages of protoplanetary disk formation crucially important. Here wefocus on dust growth and pebble formation in a protoplanetary disk that isstill accreting from a parental cloud core. Methods. We have developed anoriginal three-dimensional numerical hydrodynamics code, which computes thecollapse of rotating clouds and disk formation on nested meshes using a novelhybrid Coarray Fortran-OpenMP approach for distributed and shared memoryparallelization. Dust dynamics and growth are also included in the simulations.Results. We found that the dust growth from $\sim 1~\mu$m to 1-10~mm alreadyoccurs in the initial few thousand years of disk evolution but the Stokesnumber hardly exceeds 0.1 because of higher disk densities and temperaturescompared to the minimum mass Solar nebular. The ratio of the dust-to-gasvertical scale heights remains rather modest, 0.2--0.5, which may be explainedby the perturbing action of spiral arms that develop in the disk soon after itsformation. The dust-to-gas mass ratio in the disk midplane is highlynonhomogeneous throughout the disk extent and is in general enhanced by afactor of several compared to the fiducial 1:100 value. Low St hinders strongdust accumulation in the spiral arms compared to the rest of the disk and thenonsteady nature of the spirals is also an obstacle. The spatial distributionof pebbles in the disk midplane exhibits a highly nonhomogeneous and patchycharacter. The total mass of pebbles in the disk increases with time andreaches a few tens of Earth masses after a few tens of thousand years of diskevolution. Abridged.

Dust growth and pebble formation in the initial stages of protoplanetary disk evolution