The Baikal Gigaton Volume Detector (Baikal-GVD) is a km$^3$-scale neutrino detector currently under construction in Lake Baikal, Russia. The detector consists of several thousand optical sensors arranged on vertical strings, with 36 sensors per string. The strings are grouped into clusters of 8 strings each. Each cluster can operate as a stand-alone neutrino detector. The detector layout is optimized for the measurement of astrophysical neutrinos with energies of $sim$ 100 TeV and above. Events resulting from charged current interactions of muon (anti-)neutrinos will have a track-like topology in Baikal-GVD. A fast $chi^2$-based reconstruction algorithm has been developed to reconstruct such track-like events. The algorithm has been applied to data collected in 2019 from the first five operational clusters of Baikal-GVD, resulting in observations of both downgoing atmospheric muons and upgoing atmospheric neutrinos. This serves as an important milestone towards experimental validation of the Baikal-GVD design. This analysis is limited to single-cluster data, favoring nearly-vertical tracks.
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