FWIW I'm noy sure early morning is the best time to ride it.
When we visited a couple weeks back it seemed most reliable around noon or just after. If you go for opening then you have to fight the crowd and then hope it actually opens with the park. They also seem to add trains earlier in the day which adds 20-30mins.
Most people seem to flock to Hagrid's at park opening. You're better off doing the other rides which have no queue (basically every ride if you go left at port of entry), then by the time you reach Hagrid's it will be noon :grin: