Tinfoil Hat, as I point out Uriel has an overview of the Multiverse, but can hardly intervene in any particular universe. That means that Uriel can do the slightest of nudges in a universe where it will do the most good. The Dresden we see is the Dresden who is going to win, all the others failed, and we don’t see them (until Mirror Mirror).
We know Uriel has nudged this Dresden definitely by providing him with Soul Fire in Small Favour and a fully fit Michael in Skin Game. I suspect turning him down in Changes was a nudge towards the Winter Knight Mantle given that Sanya saved him, and the same in Battle Ground saving him from killing Murphy’s killer.
I think Uriel was responsible for Mouse ending up with Dresden, mouse is semi-divine himself, another nudge. We don’t see for example the universe where Harry gave Mouse back to the brother, despite Uriel’s nudge and Harry died at the hands of the black court vamp security guard. By Peace Talks Harry is recognising some of these nudges and anticipates them, he isn’t surprised Sanya is in town.
Uriel’s involvement with This Dresden I think dates from when Harry met Michael, those universes where Harry never met Michael or either never existed are all effectively dead ends from Uriel’s point of view. Uriel doesn’t need to intervene earlier than this because free will across a multiverse means at least one Dresden gets to the point of meeting Michael. He just has to wait and see.
Mab isn’t in a similar position she has only one universe to play with but she has a greater scope of action in that universe. She isn’t an Intellectus so she won’t know Harry from Tom or Dick unless and until he comes to her attention. Lea was aware of Harry from his birth, but Lea had her own agenda for Harry, a universe where Harry Dresden became a Furry. If Mab was involved with Harry it was most likely when Mister came into Harry’s life and he was Mab’s spy (Malk Changeling theory) around 1997. If so this may have been just after Harry met Michael (we aren’t given a timing for this but it would be around 1997 given Misters Age ) which would mean Uriel tipping Mab off about Harry. One of Harry’s memories of his father was of him picking up an abandoned kitten and nursing it back to health. I wouldn’t put it past Mab to rummage around in Harry’s memories and then selecting a Malk Changeling Kitten cut off the overlong tail and leave it for Harry to find, as a spy behind his threshold, separate to Lea.
Mab only becomes actively involved following Grave Peril which gives her the opportunity to hijack Leas agenda and her bargain with Harry. Winter Law would have prevented her involvement in Leas bargains before this. This gave her a handle on Harry for the first time.