I assume that:
- most christians believe in a single one god (monotheism); and
- that this god is the christian god.
In that case, how do you know that the gods in other monotheistic religions do not exist?
How do you know that there are not multiple gods (polytheism)?
What do you mean by "other monotheistic religions", you mean Judaism and Islam, the Abrahamic religions?
It's the same God. The Jewish God and the Christian God are the same God, the Muslim God is also the same.
We are all talking about the God who created all things, the one and only, who made Himself known to Abraham and who spoke through the Prophets.
Judaism, Christianity, and Islam do not worship three different gods, but refer to the same God, with different ideas about Him and what He has done.
In Christianity this God is Holy Trinity, and has made Himself known to us in and through the Person of Jesus, who is both the Incarnate Logos/Son, second Person of the Trinity, and the Christ, the Son of David.
But it's the same God Jews worship (incompletely because they deny He is Trinity and that Jesus is the Incarnate Son and the Christ) and the same God Muslims worship (incompletely, because they deny this God is Trinity and that Jesus is the Incarnate Son).
What Christianity confesses isn't a new and separate God from the God worshiped in ancient Israel and by the Jews, but rather the fullness of this God's revelation in the Person of Jesus.
There are non-Abrahamic monotheistic positions; certain Hindu interpretations of Brahman are more-or-less monotheistic; the Christian view would be either A) they've regarded a false non-god to be God or B) they have rightly recognized that there is only one God, but the knowledge of the one God is faulty, incomplete, and Christianity offers the full picture which cannot be known apart from the Gospel.
In the Acts, St. Paul uses the altar dedicated to the "unknown god" as a way of reaching out to the Greek pagans, whose philosophical traditions at times did regard there to to be a true, one God, but such a God was unknowable and distant--Paul explains that the true God is not distant and unknown, but has been known--He's the God of Abraham, Isaac, and Jacob, the God who has made Himself known in and through Jesus. Paul even quotes some of the Greek poets, saying, "In Him we move, breathe, and have our being" and "we are His offspring" and "He is not very far from each of us" all these poets are referring not to Israel's YHVH but yet Paul directs these poetical and philosophical sentiments back to YHVH, to the God of Abraham, Isaac, and Jacob, the One who is known in and by Jesus the Christ, the Logos of God, in whom we can know God for God meets us in Jesus and in the Church He founded.
-CryptoLutheran