We examine the emission from optically bright gamma-ray burst (GRB) afterglows, as the Ultraviolet and Optical Telescope (UVOT) on the Neil Gehrels Swift Observatory first begins observing, following the slew to target the GRB, while the pointing of the Swift satellite is still settling. We verify the photometric quality of the UVOT settling data using bright stars in the field of view. In the majority of cases, we find no problems with the settling exposure photometry, but in one case, we excise the first second of the exposure to mitigate a spacecraft attitude reconstruction issue, and in a second case, we exclude the first second of the exposure in which the UVOT photocathode voltage appears to be ramping up. Of a sample of 23 afterglows which have peak V magnitudes <16, we find that all are detected in the settling exposures, when Swift arrives on target. For nine of the GRBs, the UVOT settling exposure took place before the conclusion of the prompt gamma-ray emission. Five of these GRBs have well-defined optical peaks after the settling exposures, with rises of >0.5 mag in their optical light curves, and there is a marginal trend for these GRBs to have long T-90. Such a trend is expected for thick-shell afterglows, but the temporal indices of the optical rises and the timing of the optical peaks appear to rule out thick shells.