The Restaurant Scene

They had no reason or desire to kill Michael. He was considered a 'civilian' up until the time he kills Sollozzo and McCluskey. That's why Sollozzo asked for Michael to represent the Corleone family at the meeting . He was just supposed to hear Sollozzo out and deliver the message to Sonny. Sollozzo never suspected it would be a hit because it was known that Michael was not directly involved in the family business. He was thought to be incapable of cold blooded murder in spite of the fact he was a war hero and was wounded in combat.

Also, there was a 'negotiator' which was a bit of a misnomer. It's not explained in the film but in the book there is an Italian family named Bocchicchio that basically acts as hostages when a meeting such as the one between Sollozzo and Michael take place during a mob war. The Corleone family holds the hostage and if Sollozzo should for some reason kill Michael the Corleones would then kill the hostage. Then the Bocchicchios would go after Sollozzo, not the Corleones.

Meeting in a public place so Michael would feel 'safe' was just a ruse to be able to plant the gun. In fact, it was Michael's idea.

Just to add to the earlier answer about insisting on a public place being a ruse for the gun to be planted in advance - asking for a reasonable condition like that (somewhere Michael would feel safe) also makes it more convincing that the Corleones were going along with the truce talks.
If they'd just agreed to the meeting without question, it might have made the enemy more suspicious that they were up to something or planning something.

In addition to what was said prior - remember they didn’t kill Hagen when they had him captured. Sollozzo tells Hagen, “don’t worry, I know you’re not the muscle.” They had a code where they killed only those who were more involved in the fighting, like soldiers in a war. At that time, they saw Michael as just a civilian, which is why they had no desire to kill him at that time