I would say no.
Page 3, "5) Performing Actions":
The player who has won the offering bid on the first God can perform, in the order of his choice, the actions specific to that God, and use a Mythological Creature by paying the cost corresponding to each of those actions.
The actions are the following:
• Call upon one or more Mythological Creatures (all Gods except for Apollo)
• Recruit (all Gods except Apollo)
• Build (all Gods except Apollo)
• Special action (all Gods except Athena and Apollo)
• Increase revenue (Apollo)
The 4 main Gods work in the same way. Only Apollo is different.
It is possible to alternate actions (example: recruit, built and recruit again).
When the player is done with his actions, he places his offering marker
As I read the text, you pick one action and do that to its completion before choosing and resolving another one. In this case the player hopped onto Pegasus' back and flew to an island to do battle. He couldn't buy another mythological creature since he was still resolving the first one.
What he could've done is buy the Sylph first and resolve its action fully, then buy Pegasus and fly to battle.