In which cases can we use definite article before 'God'?
Assuming you're referring to monotheism, then "the God" can be used in phrases like "the God of" or "the God who/that", "the God over" and similar constructions, e.g.:
Hebrews 13:20 KJV: Now the God of peace, that brought again from the dead our Lord Jesus, that great shepherd of the sheep, through the blood of the ...
2 Samuel 7:26 And let thy name be magnified for ever, saying, The LORD of hosts [is] the God over Israel: and let the house of thy servant David be established before thee.
1 Kings 18:24 And call ye on the name of your gods, and I will call on the name of the LORD: and the God that answereth by fire, let him be God. And all the people answered and said, It is well spoken.
EDITED TO ADD:
There is no logical contradiction in using the definite article before an (arguendo) singular being. In the phrases like "the God of peace", the phrase isn't being used as a specifier as to which god. It's being used as a descriptor of the attributes of that god.