"I wish I was born earlier" - this is correct.
"I wish I was born in olden times" - you don't need "the"
"I came early into the world" this is a little out of place compared to the other 3 phrases you typed, so I'm going to assume what you mean is equivalent to "I wish I was born earlier" which is most correct to say. Unless you mean the opposite in which case say "I was born too early"
"I was born a generation too soon" This looks good to me! Nice work.