Is that "best?" If so, then, yes. Best physical evidence is 10th Century. Other documentary evidence suggests that it has a provenance back to the 5th Century. Certainly, any of these are older than the oldest C14 test date of 1290AD, 13th Century... which calls into question the accuracy of the C14 dating tests.
In order for this shroud to be the burial cloth of Jesus (as many believe) it would have to be from that time period, place, and shown that the burial cloth was important enough to the people at the time to preserve it, and that the present day shroud is in fact that cloth and not an artist’s medieval work (as there is evidence for).
And then there is what one might call, “chain of evidence”.
So it could be just as easily be said that the C14 tests call into question the reliability of legend, stories, writings about this shroud.
It appears that the Turin Shroud is not a burial cloth of Jesus even if it’s origin is unknown