Traceability of a mature tree to its original seed via DNA

As the embryo of a seed typically contains many cells, it should in theory be possible to obtain DNA from a seed without disrupting it (there may be pragmatic issues with protocol, depending on the particulars of the seed).

If you have the DNA and each seed has been produced by a separate fertilization event, then each seeds DNA would be unique and it should certainly be possible to identify an individual genetically, just like it is with animals.

Not all seeds are genetically distinct however. For example, many plants will also produce seeds asexually under appropriate conditions, a process known as apomixis. If the seeds are being produced asexually, then your only hope would be to identify different mutations in different seeds, which is a much fainter signal and likely to fail for your intended purpose.