9 AM, October 23, 4004 B.C.

John Lightfoot (1602-1675) notoriously dated the moment of creation to  9 AM, October 23, 4004 B.C. Which has given rise to the oft-quoted trope that "Closer than this, as a cautious scholar, the Vice-Chancellor of Cambridge University did not venture to commit himself."

Attempting to put a calendar date on the moment of creation is certainly mock-worthy. Even if young-earth creationism is true, it's not possible to date the origin of the world with anything near that degree of precision. 

That said, if young-earth creationism is true, or old-earth creationism, for that matter, then some of God's creative fiats are datable in principle, even if we necessarily lack the requisite information to do so in practice. On either view, God made some things by special creation. That being the case, you could, for instance, step into the proverbial time-machine and go back to the day when God made Adam. And you could even tell if it was morning, noonday, or afternoon by the angle of the sun. That's true for some other primeval events. In principle, these could be assigned calendar dates. The year, month, week, and day. Even time of day. Of course, any particular calendar is a human convention, and not a fact of nature. Yet you can measure time because there's a time to measure. 

In principle, you could to step into the time-machine and travel back to any Biblical event, although the earth might not be too hospitable in primordial time. Like a submarine or spaceship, your time-machine might need an artificial environment. Indeed, it's a good exercise for Christian readers to mentally take a ride in the time-machine, then imagine what they'd see when they step out.