The best time to do this was 1000 years ago. The second best time is now!

On a less jokey note, pretty much every living mammal has been subjected to domestication attempts at some point in history. Bears, elephants, tigers, hippopotami, moose... More often than not, there's some kind of inherent physiological reason why it doesn't work.

Some animals don't breed well in captivity (pandas, famously, but cheetahs are another classic case). Some can't handle captivity at all - the few efforts at keeping Great Whites in captivity ended with the animals bludgeoning themselves to death on the walls of their enclosures. Others are consistently too aggressive to effectively tame (zebras, coyotes, chimps, elephants, and pythons are notable for all the historic instances domestication failed for these reasons). And some simply aren't pleasant household companions - skunks, raccoons, and foxes are all notable for their powerful odors and their propensity to destroy the interiors of homes.

There's some speculation as to whether cats ever were actually domesticated successfully, or whether we've simply chosen to ignore their feral habits as such.

i read that Japan tried for a long time and lost many good people to it before giving up, long ago.

Well there are red pandas. I've always wanted to cuddle one