Sourdough is a bread product made by a long fermentation of dough using naturally occurring lactobacilli and yeasts.
In comparison with breads made with cultivated yeast, it usually has a mildly sour taste because of the lactic acid produced by the lactobacilli.
Sourdough is a dough containing a Lactobacillus culture in symbiotic combination with yeasts.
It is one of the principal means of biological leavening in bread baking, the others using cultivated forms of yeast.
It is important in baking rye-based breads, where yeast does not produce comparable results. (source)
So can hamsters eat sourdough bread?
Yes they can nibble on it, but it is not a food that has nutritional benefit for hamsters and so it shouldn’t be purposely be fed to them.