Yoichi asks, "Is it grammatically right to place an infinite article before the capitalized 'God'?"
Referring to the utterance:
“I want to acknowledge a God not just of second chances, but third,
fourth, fifth, sixth, seventh, eighth chances,”
Yoichi suggests that this might be because the word "god" is uncountable.
Well, the word "god" appears to be countable since there is a plural form, though there are uncountables with plurals: waters, cheeses, monies and so on. In this case, the plurals acquire some additional shades of meaning. This is not the case with god/gods where the plural is just more than one.
The second objection might be that "god" is a proper, not a common noun: hence the capital letter. This is true in some religious traditions, where "God" means a specific instance of a deity: generally Jewish or Christian, though Muslims do also say "God" despite pernickety objections from the rigidly righteous. Arab grammarians are also divided on this question of Allah / ilah common or proper noun - and the Arabic form also has plural, dual, and feminine forms - this supports the common noun party.
Assuming that this is a common noun, and the quote uses it as a common noun, then it must have an article either definite (the) or indefinite (a / an). So grammatically, we could not avoid saying "I want to acknowledge a God of second chances."
Since the said god is further qualified as being the one of second chances we assume that there are other gods not of second chances... which reinforces the message that this is, indeed, a common not a proper noun.
"I want to acknowledge God of second chances" would be a nonsense.
The only remaining question concerns the use of a capital letter? We know that common nouns are not capitalized.
Well, this could be "the God of Second Chances" following the same rule as "The Patron Saint of Travelers" where the entire phrase is treated as a proper noun. Or, it could be a mere barbarism: the writer, fearing to bring cosmic retribution onto the personage of the last-chance Governor, hesitates to use a small 'g' for God, not even a mythical god of second chances.
It is usage though, not grammar.