First, the DNA has to be decoded. No problem, with a big enough grant, but that's as far as we'll get. Being microscopic and extinct is a good way to keep from being found and decoded. In this case, one with a nice warm pouch is preferred. Maybe a kangaroo will do, if our tiger cub doesn't bite too much.
Habitat loss causes most extinctions today.
Ranchers converted thylacine habitat into rangeland for livestock. Livestock interests continue blocking efforts to reintroduce wolves, grizzlies, and bison in western North America. Considerable ground for wildlife could be gained if we pulled the subsidies feed bag from grazers, and stopped buying their meat and by-products, but until we restore habitat on a large scale, even wildlife that doesn't have to be brought back from the dead has no home. Contraception is cheaper. We aren't domesticated enough to keep from going bonkers in remote, desolate outposts like Antarctica.