I don't think arguing the semantics between "an" or "the" really matter that much. It has long been understood that the Establishment Clause states that the government cannot officially endorse or establish any religion at all.
However, in practice that has not always worked out because we see references to God everywhere in our government, even to the point where each session of Congress is opened with a prayer, and not too long ago when they had a (I believe) Sikh give the opening prayer, a bunch of Christians had to be kicked out because they were screaming about what an abomination it was. But I don't think it would be too hard to argue that "In God We Trust" is a religious motto, since it is referencing God. I know a lot of defenders will claim that "It doesn't say which god," but you, I, and they know which god the motto is talking about. But speaking as an atheist, it doesn't matter even if it's not clear as to which god it's making reference to, officially invoking belief in a god is de facto establishment of religion.
However, in practice that has not always worked out because we see references to God everywhere in our government, even to the point where each session of Congress is opened with a prayer, and not too long ago when they had a (I believe) Sikh give the opening prayer, a bunch of Christians had to be kicked out because they were screaming about what an abomination it was. But I don't think it would be too hard to argue that "In God We Trust" is a religious motto, since it is referencing God. I know a lot of defenders will claim that "It doesn't say which god," but you, I, and they know which god the motto is talking about. But speaking as an atheist, it doesn't matter even if it's not clear as to which god it's making reference to, officially invoking belief in a god is de facto establishment of religion.
Christian apologetics is the art of rolling a dog turd in sugar and selling it as a donut.