Students, aged 17-18, at ten high schools in Kupang, the capital of East Nusa Tenggara province, are taking part in the project.
Schools in Indonesia typically start classes between 7am and 8am.
Parents have complained that their children have been left exhausted by the exercise, which was announced last month by governor Viktor Laiskodat.
"It is extremely difficult, they now have to leave home while it's still pitch dark. I can't accept this… their safety is not guaranteed when it's dark and quiet," Rambu Ata, a mother to a 16-year-old, told AFP news agency.
She explained how her daughter, Eureka, has to wake up at 4am in order to arrive at school on time.
Ms Ata added: "Now every time she arrives home, she is exhausted and falls asleep immediately."
On a daily basis other students, in their school uniforms, can been seen walking down dark streets or waiting for motorcycle taxis to make their classes.
Local lawmakers have challenged the Kupang project, demanding the Indonesian government intervene and cancel what they have labelled as a baseless policy.
But authorities have resisted any criticism and extended the trial to the local education agency. Consequently, civil servants must also now start their day at 5.30am.
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