... at what exact time of the day the UN charter became official?
Article 109 of the original charter, which since subsequent amendments is Article 110 in the current charter in 2021, says
- The present Charter shall come into force
upon the deposit of ratifications by the Republic
of China, France, the Union of Soviet Socialist
Republics, the United Kingdom of Great Britain
and Northern Ireland, and the United States of
America, and by a majority of the other signatory
So you'd have to know the exact times of deposit of ratifications of each of the fifty nations represented at the conference of 26 June 1945 at which the charter was signed.
It may be that these times were not recorded.
The UN only says
It had therefore been provided that the Charter would come into force when the Governments of China, France, Great Britain, the Soviet Union and the United States and a majority of the other signatory states had ratified it and deposited notification to this effect with the State Department of the United States. On October 24, 1945, this condition was fulfilled and the United Nations came into existence.
I imagine that people didn't turn up in the middle of the night to deposit their ratification - assuming they were in paper form. So you can expect it probably occurred in reasonable working hours.