Lucky for me that this is a major aspect of my Athenian Empire timeline!
Step 1: Athens needs to either avoid the Pelo War or manage to score a major land victory BEFORE the plague hits Athens. The latter will bring the cities back to semi-equal terms and reduce that famous Lacadaemonian hubris.
Step 2: (in my TL at least) Have Sparta call upon Persia as per OTL, but have the Shahanshah attempt to conquer the weakened and war-weary states of Greece instead. This will force some measure of Pan-Hellenic cooperation and an alliance between the Peloponnesian and Delian(Imperial Athenian) Leagues(with a large measure of Athenian rhetoric and pathos harking back to Atheno-Spartan cooperation at Marathon and Thermopylae no doubt

).
Step 3: Add a couple of barbarian invasions to keep the alliance (which was hopefully more centralized and fair than previous 'Hellenic leagues') intact for a century or so. With Athens and Sparta working aside each other so closely, it's likely that Thebes will be successfully kept under heel and that the Alliance will prove profitable for both Poleis.
Step 4: Read my timeline: The Lance of Poseidon: An Athenian Empire Timeline

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(Yes, I know that was a shameless plug!)
Thanks for the question and I hope that I proved useful.
Sincerely,
~Ash