The famous Christian theologian, St Thomas Aquinas ( 1225-1274 ), in his book Summa Theologica gives 5 'proofs' ( quinque viae ) for the existence of God, and the famous Indian philosopher, Udayanacharya ( 12 century ), in his book Nyaya Kusumanjali gives 9 'proofs'.
All these 'proofs' are based on inferences ( which is called 'anumana pramana' in Indian philosophy ), and not on direct perception ( called 'pratyaksha pramana' or revelation ).
The problem, however remains : what to do with the question posed by Ivan Karamazov to his younger brother Aloysha in Dostoevsky's famous novel ' Brothers Karamazov ' : if there is a God, why do many children suffer ? ( see my blog ' Dostoevsky and the cold weather '). Millions of children who have done no harm to anyone, are yet hungry, shivering in the cold, often beaten cruelly by elders, deprived of good education and love and affection, and homeless ? If there is a God, why does he not give these children food, proper clothes, a home, proper education, love and affection by everyone, etc ?
So if there is a God, he is either all powerful, or good, but he cannot be both