Hi Eunbin Yes adding 'very' adds emphasis. If you are speaking you would also place more emphasis on this word in the sentence. Kind regards Chris

Very is used to emphasize something..something significant, important or notable about that first time.

I agree with the previous comments. If it is something special, then you would say it was your "very first time." My first time eating a hotdog was not a big deal. Getting my college degree for the very first time, was important.