Why is ...d5 the best move for Black?

Question

I am learning chess and came across this position. Stockfish 11+ HCE (Depth 32/99) and Stockfish 13 (Depth 31/47) both says ...d5 is the best move for Black. But the next move is exd6 e.p., leaving White's pawn at d6, defended by the e4-Knight and Queen, so Black cannot recapture it immediately with Bxd6.

Following along with the engine, Black doesn't really attacks the d6-pawn until at least 10+ moves later. So why did the engine suggest Black sacrifice the only central pawn it has for no apparent reason (at least to me)?

[FEN "r1bqkbnr/pp1p2pp/8/1p2P3/4N3/8/PPP2PPP/R1BQK2R b KQkq - 0 8"]
1. e4 e5 2. Nf3 Nc6 3. Bb5 f5 4. d4 fxe4 5. Nxe5 Nxe5 6. dxe5 c6 7. Nc3 cxb5 8. Nxe4

Answer 1

10+ moves later is enough! Note that material-wise, Black is already winning. The sacrifice Nc3 is far too speculative. What is the worst thing that could happen to Black? Nd6+, walling him in, or even followed by some Re1+ after exchange on d6. Thus, rather sacrifice a pawn while White hasn't even castled, than allow any swindles.

Answer 2

If you look at the position after move 8, Black is up material but has a relatively uglier position. It is in Black's interests to improve his position and if it involves giving back an adequate amount of material, then so be it. d5 forces White to waste time taking back the pawn, allowing Black to start developing his pieces.