Earliest train to Kawaguchiko

Hello! I understand that there is a lot of very useful travel information on this website, but I couldn't find any information about when train services start.

I've heard that the best chance of viewing Fuji from Kawaguchiko is before 9am, so I'm hoping to be able to check the weather conditions on the day and, weather-permitting, catch an early train from Tokyo to Kawaguchiko. How early would this be possible?

Diolch / Thanks / Domo arigato!

This can easily be looked up with Hyperdia. Just enter a departure time in the middle of the night (e.g. 3am):
http://www.hyperdia.com/

If you do so, you will see that the first train connection between Tokyo Station and Kawaguchiko Station departs Tokyo Station at 4:39 and arrives Kawaguchiko at 7:44:
http://www.hyperdia.com/cgi/en/search.html?dep_node=TOKYO&arv_node=KAW...