Sollozzo made 2 serious mistakes.
1) He vastly underestimated Sonny's nature. No way was he going to negotiate a deal with Sollozzo.
2} He vastly overestimated Tom's ability to calm Sonny down. In all fairness,Tom did advise Sonny that "if your father dies,you make the deal" as well as telling Sonny 'I think we should listen to what he has to say" referring to the meeting that Sol wanted to set up, but as we know,he was wasting his breath.
I think Sollozzo really believed that the backing of the other Dons would protect him. Granted,as a non-made guy,he could not have unilaterally hit Vito without some kind of approval,but his biggest error was in overestimating his own position as the indispensable link between the supply and distribution operations. As we see later during the 5 Families meeting with Vito,the absence of Sollozzo made absolutely no impact on the decision to organize the drug trade nationwide.
No question that Vito had to go. the potentially enormous profits to be made were much bigger than one Don,even one as respected as Vito.
I do have a question though. Doesn't the execution of a sitting Boss require Commission approval? Usually the accepted justification is some type of self defense,i.e., "he is planning to hit me" or some other overtly egregious offense against 1 or more fellow Dons. In this case, Vito didn't attack anyone or do anything of the sort. He merely obstructed. So what was the justification used to give Soll the green light?