How early do the trains and lifts run in Sept?

Hi all,
I am planning my trip to Switzerland for September. I am staying in Murren for the bulk of my stay. I'm having trouble finding lift and train schedules for that region. I have found some for the rail lines, but not much for the lifts.

I am trying to find out if everything will be running early enough for me to leave Murren to be down to Interlaken by 09:00 AM to catch a train. There are other trains I can take later out of Interlaken, but I was hoping to take the Golden Pass train to Montreux and then on to Geneva to catch a 20:30 flight to London. I'm trying to find out if this plan is reasonable or if I should plan a different route.

Thanks for your help!

The first train from Mürren to Lauterbrunnen departs at 6:06 am

Here is a link to the schedules for the mountain transports, Mürren outbound specifically

http://www.jungfrau.ch/en/sommer/tourism/travel-information/timetable/muerren/journey-back/