Which existentialist philosopher believed that existentialism and god could co-exist?

The answer to tis is Soren Kierkegaard.
Siren Kierkegaard born in the year 1813 and died 1855. He was a Danish philosopher, theologian and psychologist. He is considered by some to be the father of existentialism both theistic and atheistic. He wrote that faith is not a decision based upon evidence because the level of evidence required is unavailable.
He argued that doubt is an element of faith and it is impossible to find any objective certainty about religious doctrines such as the existence of God.

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It taught people how to live a good life, but not what to believe.