The assumption that first came to my mind after reading the questions were:
a. the furniture was not purchased in later i.e. years after the building was constructed
b. They were not antique furniture which was not purchased before the building was constructed.

If any of the above is true it means that the furniture cannot be used to determine the age of the builiding.

Which of the following is an assumption on which the argument depends？

(A) The timber used for construction purposes in ancient times was made from very old trees- Additional info- OUT
(B) The timber that was used in ancient building construction had not, prior to being used in the construction of the buildings, lain unused for an indeterminable amount of time- Yes this works- Correct
(C) The growth rings of any tree felled in a given year are identical to the growth rings of any other tree felled in that year- Other tree- OUT of scope
(D) The oldest of the ancient buildings that survive to the present day were constructed of the most durable woods-OUT of scope
(E) Ancient builders did not use more than one type of wood for the construction of a given building-OUT of scope

Hope this helps!