How do you say 'dates back to' in Mandarin? What is the best way of expressing 'dates back to' in Mandarin? e.g. the family's lineage dates back to 1720..etc
'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.