They'd kill him for it.
The only way he could get away with this is if he had already been president for quite a while and had slowly been building a very visible case against Israel, then began this investigation. Then the whole world would know who did it. If he did it too early in his term it would get buried with the flurry of all the other activity he would be engaged in.
Trump has shown a very clear pattern. He only responds if someone hits him first. Israel of course would hit him at some point, and he would escalate it. An investigation into the USS Liberty would be part of that escalation should things get to that point.