Time before early morning, before sunrise is called Brahma Muhurtham, which means that it is the time to worship God. At that time, all the people are in deep sleep and nobody will disturb you.
The atmosphere is sacred because the vibrations of mind involved in world matters are not emitted from the people since they are in deep sleep. Mind is also a form of energy. Mind disappears in deep sleep. The atmosphere is not polluted by the radiations of worldly feelings. At that time devotees awake and pray God. Their pure mental rays pervade all over the world and make the time sacred. Thus it becomes congenial and encouraging atmosphere.
After sunrise people awake and the materialistic mental radiations are emitted through their physical senses. The atmosphere is polluted. People will disturb you dragging you to materialistic discussions. Even by seeing face, you will be affected. If you see a devotee, you become sacred. The mind and body are inter-related. Since mind is energy and energy is matter, even if you see the body, the mind in that body is emitted out affecting you. Therefore, avoid even the vision of materialistic people, not to say about their touch, conversation and co-living.
After sunrise when you worship God, close your eyes to avoid such people. But, their mental radiations spread all over the cosmos and are inevitable. It is better to walk in the early morning while singing devotional songs. Morning walk is good for health. Apart from this, the mind desires dynamic condition of the body. The body was in static condition all over the night. Mind is always for a change. Satisfy the mind and you should not unnecessarily control the mind when it is not necessary.
You can pray God even without bath. Veda, Gita and the very first verse of Sandhyavandanam say that God can be worshipped irrespective of physical formalities. After some time body is tired and the mind needs rest. By that time, sunrise is over. Now you sit at a place and worship God closing your eyes. Thus the time has its own invisible effect on the spiritual effort. Sattvam is prominent in the early morning. Rajas is prominent in the day time. Tamas is prominent in the night. Therefore early morning is the divine time called as Brahma Muhurtham.