”Research has been ongoing since the 1960s to determine what the proportion of 14C in the atmosphere has been over the past fifty thousand years. The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age
[…]
Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its 14C to decay below detectable levels, fossil fuels contain almost no 14C, and as a result there was a noticeable drop in the proportion of 14C in the atmosphere beginning in the late 19th century. Conversely, nuclear testing increased the amount of 14C in the atmosphere, which attained a maximum in about 1965 of almost twice what it had been before the testing began.”
Not 100% sure, but for someone that just died, you might be able to do it with their brain, as brain cells are hardly ever renewed. For a living human I don't think there is any way that's non-invasive.
I recently tried to read up on the topic and everything I found stated that brain/nervous cells are generally barely regenerated and can stay with you your whole life. Granted, most articles trace back to this source[0] from 1967, but if newer information exists, they've done a really bad job at spreading it.
[0]: https://bionumbers.hms.harvard.edu/bionumber.aspx?&id=101940