Judging by the phrases you picked, I assume you are looking for the phrase "Given the fact...". That is the correct one, in the context you are looking for. "Given the fact..." is a loose expression used to describe the information used as a basis for a point you are about to make in an explanation or critical analysis. "Giving the fact" I personally have never seen, conversationally.

Victor Xie, I agree with 雲小泉. ‘Given the fact’ is a collocation and the more common of the two, but 'giving the fact that’ is grammatically correct and also makes sense. Here is my reasoning. -Given the fact that The past participle “given” can have the meaning “granted as the basis of a calculation” or ‘assuming as actual or hypothetical”. Examples Given that all are equal before the law, women have the right to vote. Given the fact that A = B, and B =C, then A must equal B. It can also have the meaning “considering” or “in view of”. Examples. Given that she worked as a teacher all of her life, it is surprising that she is against building a new school. Given the fact that most people do not have a disaster plan, we are urging family, friends and caregivers to get prepared now before a natural disaster strikes --------- -Giving the fact that The verb “to give” has many meanings. One of them is “to state or put forward and argument” or “ to offer for consideration or acceptance”. There is no reason why you cannot use it as a present participle with that meaning. Examples The basis functions form a partition of unity, giving that the sum of the output of the basis functions is always one. Giving the fact that you had to do a repair to the operating system, and it is now running slow and is slow to respond, there is obviously something still not quite right with it.

Given the fact. This is the way we say that phrase in America. Giving the fact doesn't make much sense. An example sentence: Given the fact that I'm an American native English speaker, you should listen to me.

Both are correct.

Given the fact that he is a quadriplegic, and there is no wheelchair access to the building, I am not surprised that he was angry that the meeting was held there. You can't blame her for telling the truth in court, she was just giving the facts. We never say 'Giving the fact' only 'Giving the facts' Given the fact and Giving the facts are not interchangeable.