Can the Researcher transfer cards to another player on her very first turn, in other words, while still in Atlanta? Seems like this gives too much of a head start at beginning of game.
Yes, it is perfectly legal for the researcher to share cards on the first turn but it is still somewhat limited, as it is limited to the cards that the player starts with. While it does sound powerful at the start, it should be remembered that it does limit the amount of damage that can be controlled on the first turn if it is spent sharing knowledge. Not to mention that if you are in a 4 player game it would only change someone's hand by 1 or 2 cards, depending on which colors they match in the other players hands, which isn't that large of an advantage when you need 5 cards to do a cure.
2 players: 4 cards to give
3 players: 3 cards to give
4 players: 2 cards to give
When doing the Share Knowledge action, the Researcher may give any City card from her hand to another player in the same city as her, without this card having to match her city. The transfer must be from her hand to the other player’s hand, but it can occur on either player’s turn.
Yes, the ability to give city cards to another player in the same city is a big advantage of the Researcher. There is no rule that forbids to use this ability in the first turn.
Note that when playing with only the Researcher and Scientist, this ability is even more powerful. The Researcher can give any city card, and the Scientist only needs four city cards to cure a disease. This makes it quite easy to win the game even on Heroic difficulty level (using 6 Epidemic cards). Both characters would stay mostly in or around Atlanta and quickly develop the four cures, without caring too much about outbreaks.
I have to admit that this feels a bit too powerful indeed. It does not only give a head start, but makes this duo almost invincible. But like Joe mentioned in the other answer, this advantage reduces when playing with more players. In that case I think the game is much more balanced.