Hmm. I tend to think that Sollozzo approached Paulie before the meeting. Paulie had missed multiple days of work and it was confirmed that he had been in contact with Sollozzo. Sollozzo also knew when and where to pick up Tom. So I think he had been watching the Corleones for a while and just put his plan into action once Vito declined the offer.

"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming

Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.