The doctor is the related to Hope, something which is truly timeless and everlasting, something which changes forms but isn't lost to people. it starts from the day you're born and stays with you till the day you die. I feel just like the toy master, hope saw a dwindling universe and had an immensely fun idea, "what if I send one of my children there and see what happens". And that's what the doctor who universe is, I presume that there would've been conditions on how the child could've been sent, like maybe there was a restriction on what it can remember about and what powers are allowed to him. but overall that's what he is in essence.