As mentioned, when he says that all men are created equal, that they are endowed by their creator with certain unalienable rights, I assume he’s talking about god. The reason I say this is because god made all human beings to be equal. Whether they thought everybody was the same was their choice. It does need to be noted that the Declaration of Independence is not this countries legal document. Therefore it has no authorities over law and this document was just necessary for its time. There seems to be no true religious faith because it could be taken as both ways and there’s always that second opinion.
In conclusion, some people do think that the Declaration of Independence declares that the United States is built under Christianity because it mentions Nature’s God and Creator a few times in the document. The Nature’s God is going back to the Divine Right during the Enlightenment period. These are barely compatible with Christianity. When Thomas Jefferson mentions creator he might not even be talking about god. No one will ever know unless they go back to the 18th century and go back when they first wrote this document.