Gambits against the caro kann

I'm finding it very difficult to find a gambit against the solid defense. Hard to find something which promotes aggressive chess at all when faced with it.

1.e4 c6 2.d4 d5 3.e5 Bf5 4.g4...

Fantasy Variation.

There are a couple of gambits of varying degrees of respectability.  

Since you are a premium member, you can look at Simon Williams's video on the Hill Billy attack if you're interested.  Simon always give colorful variations if nothing else.

I've been playing the Slav for some time, but since it transposes sometimes into it's 1...c6 cousin, the Caro-Kann, I decided to give the Caro a try as my main defense against 1 e4.  I find that it's harder, as Black, to gain the initiative but it's also much more forgiving if you make a couple passive moves instead of better, more aggressive moves.  I like it so far, though you have to work hard as Black not to get too cramped to shift your defense as needed.

It's also got built-in plans that you should consider disrupting as White: Black wants to get the QB outside his pawn chain and exchange it when the opportunity arises, take an opponent's P with your QP when practical so he can post a N at d5, take away e5 and c5 as possible opponent N-outposts, play c6-c5 when he has developed enough to do so and attack the Q-side or, if his opponent played the advance variation and is allocating to much protection to the based of White's center-pawn chain, look at f6 and a K-side push.

As white any gambits or other moves that disrupt those plans are what I look for when playing the Caro Kann as White.

Thanks for an extensive lesson!  I copied the pgn of your example to my Caro-Kann computer folder and watched the first half of the the GM William's Hillbilly Attack and may try it, though ChessKing's extensive database shows that for the position after 1 e4 c6 2 Bc4 d5 3 Bb3 dxe4 4 Qh5  there were 14 White wins, 9 draws, and 27 Black wins.  I'll have to look at how the variations went from there but you have to like White's early development compared to Black!

A Quick Google also turned up some good Hillybilly stuff:

https://www.chess.com/article/view/the-birth-and-development-of-the-hillbilly-attack (GM Williams)

A live GM Simon Williams Hillbilly Attack vs a 2198 blitz opponent:

https://www.youtube.com/watch?v=FqSdZ64wTIY

A 2-part YouTube Hillbilly Attack Video series, about 31 minutes:

https://www.youtube.com/watch?v=qQWRtPHA1yE

https://www.youtube.com/watch?v=fdPTONY9uaI&spfreload=10

Crush The Caro-Kann - Chess Openings Explained (Jonathan Schrantz, St. Louis Chess Club):

https://www.youtube.com/watch?v=wUZAyFpMQxw

There aren't any particularly sound gambits against the Caro-Kann.

I don't consider the "Fantasy Gambit" mentioned above (5...exd4?! 6. Bc4!) to be a gambit. White will clearly get the pawn back; at worst immediately, and possibly a lot more if Black is not very careful.

Against 1. e4 c6 2. d4 d5 3. e5 Bf5, 4. g4 is not good at all, and it's not really a gambit.