There is a gambit for black that is not discussed enough because it is often regarded as one of the worst gambits in existence. Hikaru Nakamura ranked it as total trash in Levy's gambit ranking video. Despite all that, black has a plus score in the LiChess user database, and I have suffered some of my worst losses against this gambit. The best moves for white are unconventional and not at all subtle but reading this will help you stomp the Elephant gambit.
The best way to refute any gambit is to take the pawn. Capturing with the pawn is superior to Nxe5 because black is close to equal if all the central pawns are traded after 3.Nxe5 dxe4 4.d4 exd3 5.Bd3. The ambitious way is to capture on d5 and pin the e-pawn to force black to defend against 4.d3. In some lines the d5 pawn prevents Nc6 and makes Qb5+ very strong. I also show one of my games where Qb5+ is a stupid move that only helps black develop.
Against 4...f5, the best move is still d3. The advantage of f5 is that the e4 pawn can be defended an additional time, but the downside is that it is a waste of a move. White can now play Nc3 later because of the Qb5+ reply against Bb4. Although white does not win a piece in the end, white has a positional advantage with more active pieces, better development and open files for the rooks after O-O-O.
This game was extremely disappointing because I played 8 moves of theory and still lost in 10 moves. This gambit should be taken seriously and discussed more openly. Studying this opening will not help you win tournaments but understanding the nuances of move orders and the dxe5 and Qe2 plan will help you score some easy wins in blitz.