Waking up in the early morning has a tradition within Buddhism. The early morning is quiet. The world has not woken up yet. Nice. In the early days before there were big cities, especially way back in the Buddha's time, wandering monks and nuns would live in the forests and parks, yet close to cities, because they had to get food. The early morning time was special, if they got up early they could meditate with the quiet. In the middle of the day, living in the forest close to a town, you might hear all the hustle and bustle, the carts going by, the music shows coming and going and everything else. But in the early morning before the sun rose it was quiet, so it was a really nice time to meditate.
It is also a time of day when your stomach is empty. Sometimes you have probably noticed yourself, that if you eat too much, you have difficulties meditating. The stomach just feels uncomfortable and you may even have to go to the bathroom in the middle of the sitting or whatever. So in the early morning when your stomach is relatively empty, this disturbs you less.
As well, traditionally when monks went for food, they were supposed to go as soon as there was enough light. The reason why they went early was so they were not in the town when everything was super busy. They would go into town and leave before things got too busy. So another reason for the monks getting up early, before it was daybreak was in order to meditate before they went out to get food.