How do you say 'dates back to' in Mandarin?
'Dates back to' is usually translated into '追溯到', which literally means 'trace back to'.
When used in a sentence, people usually add 可以 (can/may) or 要 (have to) before 追溯到, for example:

这个城堡要追溯到罗马时代。
(The history of) this castle dates back to Roman times.
这个家族的历史可以追溯到十七世纪。This family can trace its history back to the 17th century.