Laser wakefield acceleration (LWFA) using PW-class laser pulses generally requires cm-scale laser-plasma interaction Rayleigh length, which can be realized by focusing such pulses inside a long underdense plasma with a large f-number focusing optic. Here, we present a new PW-based LWFA instrument at the SG-II 5 PW laser facility, which employs f/23 focusing. The setup also adapted an online probing of the plasma density via Nomarski interferometry using a probe laser beam having 30 fs pulse duration. By focusing 1-PW, 30-fs laser pulses down to a focal spot of 230 μm, the peak laser intensity reached a mild-relativistic level of 2.6 × 1018 W/cm2, a level modest for standard LWFA experiments. Despite the large aspect ratio of >25:1 (transverse to longitudinal dimensions) of the laser pulse, electron beams were observed in our experiment only when the laser pulse experienced relativistic self-focusing at high gas-pressure thresholds, corresponding to plasma densities higher than 3 × 1018 cm-3.