"In the first place" is used in two ways : to mean 'firstly', in a statement which is going to be followed by another one giving further support to a case or argument e.g. I didn't do the work, firstly [in the first place] because I didn't have the materials, and secondly, I wasn't able to get to the place. The other use of 'In the first place' i.e. 'to begin with / to start with' is when referring to something that has happened, which may form part of an explanation or an enquiry. 'He should not have been there in the first place' : implies that if he had not been there, something negative [undesirable] may not have happened. 'Why was he there in the first place ?' 'If I had not done the work in the first place, this would not have happened.' 'For the first time' is not used in the same way.

"How can I use "in the first place""? It means "firstly" and is often used when countering an argument e.g. "In the first place, your argument is wrong because...." You can also use it generally as a synonym for "firstly"

They do not have the same meaning. "in the first place" Why didn't you tell me in the first place? (meaning why didn't you tell me in the beginning) "for the first time" I visited California for the first time. (meaning I had never been there before)