Thyme is a evergreen herb that is often used for ornamental reasons, medicinal and in culinary dishes.
The most common type is the Thymus vulgaris.
Thyme is sold both in a dried form and also fresh. Because it is grown fresh in greenhouses it is possible to get thyme all year around at a reasonable price.
This herb is part of the mint family and is also related to oregano genus Origanum.
It can actually last up to many months if frozen correctly [Source] or a two weeks in the fridge.
So can hamsters eat thyme at all?
Yes, it is fine for them to eat. However do not give them too much as it could make them sick.