The SuperKEKB electron-positron collider is being commissioned at KEK to study a new physics in the B-meson decays. In order to accomplish this purpose, the luminosity of 40 times of the highest luminosity record at KEKB, 8$\times$10$^{35}$ \lum is necessary. We have applied a novel “nano-beam scheme” to squeeze the beta function at the interaction point (IP) down to 1 mm in the vertical, 60 mm for the HER (7 GeV electrons) and 80 mm for the LER (4 GeV positrons) in the horizontal direction, respectively. We have tested $\beta_y^*$ of 800 $\mu$m finally and performed physics run with data acquisitions by the Belle II detector. The beta function at the IP is the smallest value for the existing circular colliders in the world. However, the design value is 0.3 mm which is still about 1/3 of the achievement. We have also applied a “crab waist scheme” which proposed by P.~Raimondi et al. to improve the luminosity performance in the nano-beam scheme. The peak luminosity of 2.4$\times$10$^{34}$ \lum has been achieved which is the highest value in the world. The vertical beam size at the IP of 224 $\mu$m was also achieved, which is the smallest beam size for the colliders. The early stage of the commissioning of the nano-beam scheme as well as the crab waist scheme in 2019 run and Spring run in 2020 is presented.