Why? Just to see a Thylacine? You'd be much better off as having visited London Zoo when they had one of their Thylacines because you'd have been able to see a whole lot more species at the same time, some of which would probably also be now-extinct if you picked your date of visit correctly.Beaumaris Zoo in Tasmania, especially around or before 1936. Unfortunately I wouldn't be born yet for the better part of a century.
If we're going with past zoos "if I'd been born then" I wish I had got to visit Montezuma's Zoo. That would have been really interesting.