We present the first search for the standard model Higgs boson (H) produced with large transverse momentum (p$_{\mathrm{T}}$) via gluon fusion and decaying to a bottom quark-antiquark pair ($\mathrm{b\overline{b}}$). The search is performed using a data set of pp collisions at $\sqrt{s}=13$~TeV collected with the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9~fb$^{-1}$. A highly Lorentz-boosted Higgs boson decaying to $\mathrm{b\overline{b}}$ is reconstructed as a single, large radius jet and is identified using jet substructure and dedicated b tagging techniques. The method is validated with the first observation of the Z$\to\mathrm{b\overline{b}}$ process in the single-jet topology, with a local significance of $5.1$ standard deviations ($5.8$ expected).