PREMISE 1: Time is infinitely divisible.
PREMISE 2: No artificial, unnatural quantity is infinitely divisible.
CONCLUSION: No time is an artificial, unnatural quantity.
In examples of artificial, unnatural quantities like weight, density, temperature and velocity, their infinite division is meaningless.
A clock is divisible, time is not, time is constant until it ends, even if it hick-ups it is not divisible.
But perhaps the devisiblity you speak of is that it once had a beginning and will have an ending, so yes divisible to a degree.
Time exists even after you die, hard to imagine but it probably does.
But perhaps time is God, the infinate never beginning because it cannot end.
Perhaps we are infinate, perhaps there is no such thing as an ending?