The earliest BTA (SAO RAS 6-m telescope) spectroscopic observations of the GRB 030329 optical transient (OT) are presented, which almost coincide in time with the first break ($tsim 0.5$ day after the GRB) of the OT light curve. The beginning of spectral changes are seen as early as $sim 10-12$ hours after the GRB. So, the onset of the spectral changes for $t<1$ day indicates that the contribution from Type Ic supernova (SN) into the OT optical flux can be detected earlier. The properties of early spectra of GRB 030329/SN 2003dh can be consistent with a shock moving into a stellar wind formed from the pre-SN. Such a behavior (similar to that near the UV shock breakout in SNe) can be explained by the existence of a dense matter in the immediate surroundings of massive stellar GRB/SN progenitor). The urgency is emphasized of observation of early GRB/SN spectra for solving a question that is essential for understanding GRB physical mechanism: {it Do all} long-duration gamma-ray bursts are caused by (or physically connected to) {it ordinary} core-collapse supernovae? If clear association of normal/ordinary core-collapse SNe (SN Ib/c, and others SN types) and GRBs would be revealed in numbers of cases, we may have strong observational limits for gamma-ray beaming and for real energetics of the GRB sources.
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