What is the proof or evidence that God exists?

Charuvaka's or Atheists claim that we cannot see (or touch or feel or smell or hear etc.) God and therefore He does not exist.  Abrahamic religions ride partially on Charuvaka's arguments to deride Hindu Gods. Hindus are confused about who is God because of the sheer number of them (33 crores?) who are all collectively referred to as God and many of them even have temples where they are worshipped and revered. But the few Hindus that know some vedanta agree that eventually there is only one God - and that it is He/She that manifests in so many forms (33 crore+) for different purposes. They also agree that He/She is in each one of us as Antaryami or Soul or Self or Atma - whatever technical jargon they want to use.  At the end of the day, 99.9% of the world, irrespective of the religion they choose to live by, wants evidence of God's existence. The lack of evidence is the primary reason why Atheists call the theists as "blind followers".

Swami Nammazhvar says there is no dearth of Gods in this world. What one accomplishes at the end of this life depends on the God that he/she chooses to worship. In other words, most of these Gods that people worship, have limitations on what favors they can give/grant to their worshippers. 

Thivaimozhi pasuram

குலம் தாங்கு சாதிகள் நாலிலும் கீழ் இழிந்து எத்தனை
நலம் தான் இலாத சண்டாள சண்டாளர்கள் ஆகிலும்
வலம் தாங்கு சக்கரத்து அண்ணல் மணிவண்ணர்க்கு ஆள் என்று
உள் கலந்தார் அடியார் தம் அடியார் எம் அடிகளே.

River Ganges Regained her Purity at Varanasi

This is the Adhi Keshav temple and the Adhi Keshav Ghat in Varanasi.

River Ganges is originally Trivikraman's Sri Pada Theertam -  the water that washed the holy feet of Trivikraman. When the Lord had taken Vamana Avatar and then took the huge form of Trivikraman to measure the lower seven worlds with one foot and upper seven with one foot, His right foot reached  Brahma's Satya Loka. Seizing this opportunity, Brahma instantly washed His foot and offered his prayers to it. This water that he washed His feet with became Ganga and is flowing as a river even today in Satya Loka.  It was this river that Bhageerata brought down to earth after performing penance. In order to regulate her flow, Shiva offered to receive her on his head and regulate the flow through his hair.  This is the first source of dosham or impurity for Ganga.

After Shiva regulated her flow on earth, she was flowing unhindered when she disturbed Maharishi Jahnu's penance. The angered rishi swallowed her. Upon Bhageerata's request, he let her go through his ears. That is how she got her name as Jhanavi. This is her second source of dosham or impurity - as she had become the uchishtam (jhoota or echil) of Jahnu maharishi.

At the Adhi Keshav Ghat in Varanasi, Swami Ramanuja during his all India digvijayam (tour) released her from those impurities by washing his feet. Ramanuja, an avatar of Adiseshan or Seshnag, thus helped river Ganges regain her purity at Varanasi.

 

Karma, Knowledge, Bhakti, Moksha

1. Balance of Karma is of two types - Punya and Papa.
2. Everybody acts/reacts according to what each person knows.
3. Actions result in Karma - either Punya or Papa based on whether the act has pleased the Lord or not. If the Lord is pleased, the result if Punya Karma. If the Lord is not pleased the result is papa karma.
4. Punya and Papa in normal circumstances have to be spent by experiencing happiness and unhappiness. When you are happy you are spending Punya karma. When you are unhappy or in pain, you are spending papa karma.
5. Each person acts by his/her independent knowledge and decision.  You are responsible for your actions, not God. Therefore one should own his/her decisions, and always think and act without making impulsive decisions.
6. What we know affects our decision-making ability.
7. Shastras, especially Smriti's describe how one should live life. Living life according to scriptures pleases God. Doing things that the scriptures tell us to avoid, or not doing what they have ordained us to do will result in Papa karma. Therefore, one must learn the scriptures to understand the Do's and Dont's so as to live according to them. Living as described in the scriptures is called Karma Yoga.
8. The cause of ignorance is Balance of Karma. As we continue doing Karma Yoga, it pleases the Lord, and by His blessings, some critical pieces of knowledge dawns upon us.
9. The newly acquired knowledge will further strengthen our resolve to continue performing Karma yoga. This results in more knowledge dawning upon the individual, merely by the Lord's grace.
10. Thus, knowledge acquired by the Lord's grace is more favorable and appropriate for one's spiritual progress than the knowledge acquired through human effort of reading, understanding, doing penance, meditation, etc.
11.  Knowledge as it matures, becomes Bhakti (Devotion). Such Bhakti will be more steadfast than Bhakti cultivated towards the Lord by human effort.
12. Knowledge and Bhakti continue to grow in the individual merely by the Lord's infinite grace. The individual continues his Karma Yoga, even as the knowledge and bhakti continue to intensify.
13. The realization that the Knowledge and Bhakti is a result of the Lord's grace helps the person to give up self effort towards spiritual growth. At that point the person performs Sharanagati or complete surrender to the Lord.
14. Upon complete surrender, the Lord wipes out the individual's remaining Karmic Balance from the timeless past or Sanchita Karma.
15. He has assured that He gives Moksha to those that surrender to Him, at the end of the very physical life the person is leading. That life becomes the individual's last birth on earth.
16. Having performed Sharanagati, the individual continues to perform Karma yoga not expecting anything else in return (what else does one need more in life, having received the assurance from the Lord that Moksha is guaranteed at the end of the life?). This is called Nishkamya Karma.
17. Such a person lives the rest of his/her life merely for the Lord's happiness and becomes interested in doing only those things that pleases the Lord - like singing for Him, cooking for Him, reading about Him, sharing thoughts about Him, extolling His great qualities, enjoying the company of others that have surrendered to Him, serving Him at his temples, serving others that have surrendered to Him, serving the Acharya that facilitated his surrender to the Lord, and merely "experiencing His grace." He is not interested in other worldly activities, accomplishments, and achievements. The Lord is his only wealth.
18. Such a person understands that everything in this world is subservient to Him, and that the world cannot exist without Him.
19. From this point onwards, as the individual slowly detaches himself from worldly life, merely by the Lord's grace, the Bhakti becomes Para-Bhakti. It is a state in which the individual is looking up to the Lord for anything he/she needs even for survival.
20. Again merely by the Lord's grace, the Para Bhakti becomes Para-Gnana. In the Para-Gnana state the individual is able to see the Lord (Darshana Samanakara Sakshatkaram).
21. As the individual ascends to the Kingdom of God in Srivaikuntham he/she achieves the final state of purity called Parama-Bhakti. In this state, the individual is unable to bear even a second of separation from the Lord.
22. All this spiritual progress happens merely by the Lord's effort and not by the individual soul's effort. The liberation of the individual soul is therefore the Lord's responsibility and not that of the individual. In fact, he refuses to intervene if the individual continues to make self-effort towards spiritual progress. Knowing this, one should not waste any more time, and simply surrender to the Lord through a qualified Acharya.