How did yuji get the midnight lost child in the first place?

At some point in Season 1 it is explained that treasure tools are transported randomly to a new host Torch when the original Mystes flame dies. Yuji is obviously the one Mystes that is essentially immortal where as other Mystes' come and go like any other Torch.

This property of random transportation is one of the reasons why Hunter Friagne did not simply destroy Yuji on the numerous occasions he had the opportunity. This is also why Shana considers destroying Yuji in Episode 1 since she does not care about Treasures other than her own sword.