  Characterizing the physical properties of dust grains in a protoplanetary
disk is critical to comprehending the planet formation process. Our study
presents ALMA high-resolution observations of the young protoplanetary disk
around DG Tau at a 1.3 mm dust continuum. The observations, with a spatial
resolution of $\approx 0.04''$, or $\approx5$ au, revealed a geometrically thin
and smooth disk without substantial substructures, suggesting that the disk
retains the initial conditions of the planet formation. To further analyze the
distributions of dust surface density, temperature, and grain size, we
conducted a multi-band analysis with several dust models, incorporating ALMA
archival data of the 0.87 mm and 3.1 mm dust polarization. The results showed
that the Toomre $Q$ parameter is $\lesssim2$ at a 20 au radius, assuming a
dust-to-gas mass ratio of 0.01. This implies that a higher dust-to-gas mass
ratio is necessary to stabilize the disk. The grain sizes depend on the dust
models, and for the DSHARP compact dust, they were found to be smaller than
$\sim400$ $\mu$m in the inner region ($r\lesssim20$ au), while exceeding larger
than 3 mm in the outer part. Radiative transfer calculations show that the dust
scale height is lower than at least one-third of the gas scale height. These
distributions of dust enrichment, grain sizes, and weak turbulence strength may
have significant implications for the formation of planetesimals through
mechanisms such as streaming instability. We also discuss the CO snowline
effect and collisional fragmentation in dust coagulation for the origin of the
dust size distribution.
