This phrase is obviously used by contemporary Christians as big proof that the Founders meant that our rights were God-given by Christian God and the founding fathers therefore intended that the US be a Christian country.
But how much was “their Creator” an intentionally ambiguous phrase at the time? Was that phrase chosen to imply that citizenship was an inalienable right by birth, instead of being lesser citizens whose rights were determined at the whims of a King?
Like how much do scholars think it was meant to mean “God given” versus “Dad given?” Or was it just designed to imply both?
The best answer here is that Jefferson was likely being ambiguous on purpose, allowing different groups to read into the declaration what they wished. Although the oft-uttered pronouncement that most of the "Founders" were Deists is somewhat overblown, in Jefferson's own case the label is pretty apt. Jefferson was known to be quite intentional about his word choice, so his insertion of the terms, "Nature's God" and "their Creator" rather than something more explicitly religious like "Our Lord" was without a doubt intentional. And given what else we know about Jefferson, he likely hoped that this sensibility would translate for a general populace and grant a sort of secular air to the Revolution. But he was not insensible to the religious character of many of his countrymen, so using an intentionally vague term like "Creator" could satisfy any Christian, Quaker, Jew, or Deist who read it.
Jefferson himself was fairly irreligious, even among other gentlemen of his Age, who tended to be somewhat more secular than many of their contemporaries. He would always count his Bill for Religious Freedom in his own native Virginia as one of his great accomplishments (a distinction, somewhat puzzlingly, he rarely gave to the Declaration of Independence). The bill, which took nine years to be enshrined in state law, removed all religious tests for office, eliminated church membership as a requirement for residents, allowed absolute freedom of conscience, and disestablished the Anglican church (and separated church and state) in Virginia. In the long run, this would become a model pattern for other states, but it's worth noting that much of New England continued to have established Congregational (Puritan) churches into the early 19th century.
Jefferson's irreligiosity would later be the source of controversy in the 1790s when tensions between his Republican faction and the ruling Federalist Party came to a head. During the election of 1800, Hamilton wrote to John Jay, “[We must] prevent an Atheist in Religion and a Fanatic in politics from getting possession of the helm of the State.” Though it is also worth noting that despite being a somewhat traditional Episcopalian, Hamilton was hardly of an evangelical mind himself--according to Gordon Wood, when asked by New York constituents why he and the other constitutional authors had omitted God from the Constitution, Hamilton allegedly replied, "we forgot."[1]
The end of the 18th century was probably as close to the low tide for religiosity as one can imagine in the United States, at least among the educated classes, especially when compared with the evangelical fervor that would erupt in the early 19th century, much to Jefferson's own chagrin. The "contemporary Christian" view you posit does not have solid grounding in historical fact, at least as concerns people like Jefferson. This is in part why it's so puzzling that modern fundamentalists like David Barton would focus on Jefferson of all people to try and squeeze into a Christian-America narrative. Jefferson's secularism was hardly a secret to his contemporaries, let alone to 21st century historians.
See also this post by /u/USReligionScholar in the FAQ about other "Christian nation" claims, and this post by /u/Irishfafnir on religious views among the "Founders."
Source:
[1] Gordon Wood, The Radicalism of the American Revolution