Can I use Star Crossed to bounce back a Fizz to before his spell resolves to counter it?

No, you cannot stop Fizz's ability by bouncing him with Star-Crossed. Once a triggered ability is on the chain, it exists independently of its source — removing Fizz from the board doesn't remove his ability from the chain, and it will still resolve normally.

Here's the sequence showing why:

1. Fizz resolves — he enters the battlefield as a permanent.
2. His "When you play me" ability triggers and is placed on the chain as a Pending item, targeting a spell in his controller's trash.
3. You play Star-Crossed (Reaction) targeting Fizz and a friendly unit. Star-Crossed goes on the chain above Fizz's ability.
4. Star-Crossed resolves first — Fizz returns to hand. However, Fizz's ability is still on the chain and independent of its source at this point (FAQ #10936, #11567).
5. Fizz's ability resolves — it still has a valid target (the spell in trash), doesn't reference Fizz's location to function, and will successfully play that spell.

Unlike an ability that references "here" or "this battlefield" (like Azir, Sovereign's attack trigger — FAQ #11183), Fizz's ability doesn't need Fizz on the board to identify anything. The trash target is still there regardless.

The only way to stop Fizz's ability is to remove the targeted spell from the trash before the ability resolves (e.g., with Disposal Order — see FAQ #11060), making the target unavailable per Rule 359.3.e.7.