I'm looking for a fast way of getting from North Wales (30-40km radius from Dolgellau) to Cambridge on a Sunday evening by public transport. I found a train that takes 6h, with a change in Birmingham and London. Is there a quicker way?
The only rail routes out of that area are either the Cambrian Line train from Machynlleth to Birmingham or the Conwy Valley line from Blaenau-Ffestiniog to Llandudno. Blaenau-Ffestiniog and Machynlleth are both similar drives / bus journeys from Dolgellau. The actual closest station is Morfa Mawddach, but it's a long, slow ride from there to Machynlleth, and you can save a lot of time by driving a little further to Machynlleth and cutting the corner (of course, if you were walking, walk to Morfa!).
At times when there's a direct train from Llandudno Junction to London and a reasonable connection at Llandudno Junction from the Conwy Valley, you can make Blaenau to Cambridge in about five hours, which is about hour quicker than any train from Machynlleth will get you there.
Unfortunately, there aren't any trains on the Conwy Valley Line on Sundays (at all; it only operates six days a week), so you'll need to go to Machynlleth. The last train is the 18:05, and takes 7h24 to arrive at 01:29 (mostly as a result of hanging around an hour in Wolverhampton); the 16:05 can make it in 5h50, ie by 21:55
If you're prepared for a longer drive, then your best option is definitely Llandudno Junction; the last train leaves at 18:24 on a Sunday, and should get you to Cambridge around midnight; the 17:25 is about 30 minutes faster because of a better change in Chester rather than Crewe.
ETA: One small bit of advice: if you get an advance ticket, consider getting an advance to London and buying a flexible ticket London-Cambridge, rather than an advance all the way. You can almost certainly walk from Euston to King's Cross faster than National Rail thinks you can, and with a flexible ticket you can just hop on the next train to Cambridge rather than having to wait for the specific one you're booked onto. London-Cambridge is £16.40 on an super-off-peak day single, which would be available for Sunday evenings - and the Machynlleth-Cambridge advance is usually going to be five or six pounds more than Machynlleth-London, so the extra flexibility shouldn't cost more than a tenner.