What is confusing is that although this is a true name and a true meaning, it does not delineate which God was with us. It just says God.
For people in the Church of Jesus Christ, this is no problem because we believe in 3 Gods, and in context we know which God was born of Mary, it was God the Son, not God the Father or God the Holy Spirit.
It becomes probematic to you because your God is 3 Persons in 1 God. So when the scriptures say God with us, you have to translate that to God the Father, God the Son, and God the Holy Spirit is with us, and the great Triune God was born of Mary.
Now I know you will have a problem with this, but sorry, that is your believe about God. You cannot have your cake and eat it too. If your God is made up of 3 distinct Persons, then all of them existed in the baby body born of Mary. You cannot say well we believe in the great Triune God, but at the birth they were not all in that baby body. Sorry can't choose when they are 1 God and when they are not.
So rather than being sorry, we are glad that we believe in the 3 mighty Gods of Christomdon.
God the Father, God the Son, and God the Holy Spirit. Their total unity in regards to their purpose make them 1 God. And we can be one with each other as they are one, if our purpose is the same also. (John 17:20-22)