Faith

You live only by faith. The Vedanta is a difficult subject, because any amount of probing lead to nowhere. All philosophies looked very logical, very acceptable, very beautiful from outside, but inside it is hollow. So, look for belief based on experience and intuition along with Reason. All living things are controlled by intelligent agency. Intelligence is the root cause of all functional aspects of all life. There is an agency that does exist, and it exists independently of the machinery of our chemical bodies.
If you see a flag blowing in the wind, you know there is wind. If the flag is destroyed, did the wind stop?

Are we programmed to question existance of God?

YES.
Humans ask complex questions such as “why is the sky blue?”, "why we exist?".
We suffer discomfort with unanswered and even not well answered questions.
Same persons, who produces complex questions and discomfort with improper answers to those questions, looks to mysticism, and science.
Let us look for belief system known for intellectual honesty. Let us look for the quality of the evidence supporting it.

Are we programmed to believe in God?

Humans are programmed to believe in God because it gives them a better chance of survival. A study into the way children's brains develop suggests that during the process of evolution those with religious tendencies began to benefit from their beliefs - possibly by working in groups to ensure the future of their community.

What to believe?

Listen for Truth, what ever be the source. Let noble thoughts reach you from everywhere [Rig Veda].
Supernaturalism - a belief in forces beyond ordinary human understanding. Check and confirm.
Try to reduce/avoid superstitions - an irrational belief arising from ignorance or fear.
Most will believe in God or Great energy/force or almighty. One can feel God's presence during focused attention, moral reasoning, prayer or meditation. Billions of people make important decisions in life based on spiritual and religious feelings and experiences. It's one of the most powerful influences on our social behavior. Religious and spiritual experiences activate brain like feelings of love, music and even drugs [from journal Social Neuroscience].

seven basic kinds of thinking

According to Hinduism there are seven basic kinds of thinking, Each of them is associated with a Hindu god. They are,
  1. Dreaming - Indra
  2. Illusion - Shakti
  3. Reasoning - Brahma
  4. Natural thinking - Vishnu
  5. Determination - Shiva
  6. Status altering thinking - Shani
  7. Compulsive thinking - Yama.

Science and religion

To believe in God or to believe in science is a choice. But people in general don't want to give up on either one of them, because they recognize that they are both very very important for life to continue. To believe in a God gives them hope, to believe in science gives them certainty.
Don't confuse scientific facts with the interpretation of those same facts.
Science and religion are not mutually exclusive. However, religion has to adapt, and believers can no longer claim their ancient scriptures as literal fact.
Science deals with the observable [distinct from the hopes and the things unseen that are addressed through faith]. It seems that the more we learn in science, the more we realize how little we know.

God, Beyond Science?

When a phenomena is explained by science, that means it can be shown to be consistent with this body of knowledge. Science is the best and most effective way we have managed to develop for finding the truth about the World. Nobody is claiming to have found any “ultimate truth”. It is not even clear what “ultimate truth” means or can be identified
Belief systems were developed by the ancients as a means to explain what the science at the time could not explain. Higher power is an extrapolation. Science deals with the natural world. God is a supernatural being (extrapolation of natural world). science breaks down, and that is where God starts.
Gods exist in the sacred or SUPERnatural space. Science is constrained to the domain of the physical universe that can be observed and measured, and whose behaviours and attributes can be empirically demonstrated with repeatable consistency. Concept of a higher power lies entirely outside that domain. There are many observable phenomenon we can’t explain, when some call them as evidence of God.
The existence of a higher power is based on faith. There’s no need for evidence if you’re a believer, and there’s no need for looking for scientific proof (or lack thereof) if you’re not a believer.