I can't remember which book it was but in some Mafia book an informant declared that the idea of Vito standing against all the other bosses and preventing them from doing something was ridiculous.

The other bosses , but especially Barzini and Tattaglia wanted to move up and usurp the Corleone power. Especially for Barzini, the Sollozzo gambit was a win-win proposition. Vito says yes and Barzini gets wealthier and more powerful. Vito says no and Barzini rallies the other families against him.

As Sollozzo said Vito's "no" was not realistic. It was telling Sollozzo that he couldn't make a living. Sollozzo wasn't going to tolerate that. As Tom mused in the book, outside of Luca, Sollozzo was the most dangerous looking man he'd ever seen.

So regardless of what Sonny said, Sollozzo had already decided to move on Vito if he gave the wrong answer.

Sonny's interjection likely made Sollozzo assume (wrongly) that with the successful removal of Vito that Sonny would more or less go along with the program, even with his storied irrational nature, because ultimately such a move was good for business. This is detailed more in the book where Sonny says that if his father died that he'd be way too busy trying to hold on to the Corleone holdings to consider expansion or revenge and that even if the Corleone Family did manage to stick together the other Families wouldn't tolerate a war launched years later purely out of spite.

So maybe Sonny's blurted comment made Sollozzo move up the planned date. Or maybe that was enough to convince a skeptical Barzini or Tattaglia to give their final blessings to the move.

"Look, his own son wants the deal!!!"