The TimeLib.h has a command to set the time see TimeLib.h
For simplicity I would put :
setTime(hr,min,sec,day,mnth,yr); // alternative to above, yr is 2 or 4 digit yr
// (2010 or 10 sets year to 2010)
In your setup routine and put in the current time (maybe 15 seconds or so ahead) download and run.
The issue will be each time the Arduino reboots the time will be set to whatever you coded into the Setup routine.
You could add a button or manual connection so on startup it will only set the time if the manual connection is connected.