  We report the results of optical follow-up observations of 29
gravitational-wave triggers during the first half of the LIGO-Virgo
Collaboration (LVC) O3 run with the Gravitational-wave Optical Transient
Observer (GOTO) in its prototype 4-telescope configuration (GOTO-4). While no
viable electromagnetic counterpart candidate was identified, we estimate our 3D
(volumetric) coverage using test light curves of on- and off-axis gamma-ray
bursts and kilonovae. In cases where the source region was observable
immediately, GOTO-4 was able to respond to a GW alert in less than a minute.
The average time of first observation was $8.79$ hours after receiving an alert
($9.90$ hours after trigger). A mean of $732.3$ square degrees were tiled per
event, representing on average $45.3$ per cent of the LVC probability map, or
$70.3$ per cent of the observable probability. This coverage will further
improve as the facility scales up alongside the localisation performance of the
evolving gravitational-wave detector network. Even in its 4-telescope prototype
configuration, GOTO is capable of detecting AT2017gfo-like kilonovae beyond
200~Mpc in favourable observing conditions. We cannot currently place
meaningful electromagnetic limits on the population of distant ($\hat{D}_L =
1.3$~Gpc) binary black hole mergers because our test models are too faint to
recover at this distance. However, as GOTO is upgraded towards its full
32-telescope, 2 node (La Palma \& Australia) configuration, it is expected to
be sufficiently sensitive to cover the predicted O4 binary neutron star merger
volume, and will be able to respond to both northern and southern triggers.
