You could achieve this by having a server block output the number of entities departed (#d) and log that signal then just look at the Values.Time variable for that signal to see when the event (in this case entity goes through the server) occurs. With the attached example RecordTime_Sample_TS.slx, execute the following code to save the signals to variables after running.
departed = get(logsout,'departed');
startTime = get(logsout,'startTime');
departed.Values.Time
startTime.Values.Time
startTime.Values.Data
