Archaeologists commonly monitor pollen types in sealed (buried) horizons—well, if the project has sufficient funding for it. From the pollen, you can discern things about the climate, the season the material was buried, etc. Only in unusual circumstances do we find seeds. Archaeologists found date palm seeds at Masada (yes, the fortress built by Herod around 35 BC and destroyed by the Romans in AD 73), and one is now three years old and more than three feet tall! (Science link, too.)