Perhaps if Truman feels politically secure enough in 1948 to officially recognize Israel very early on? That would open doors to various kinds of private assistance for a start and would have provided an air of legitimacy for the new "nation" from the beginning. Reportedly Truman had been leaning towards early recognition but Marshall's various arguments convinced him to table the idea. After that, the time never seemed right for US recognition.
Truman was sympathetic towards the Jews, as many were after the end of the war in Europe unveiled the death camps. Truman also had close Jewish friends and had even been in business with a Jew for a time after WW1.
It seems strange to us now, but there was an upsurge of vague anti-Semitic feelings in the US during the period driven mostly by the looming Cold War. By 1948 China had already been lost and Hoover had uncovered the vast Soviet spy apparatus within the country. Most troubling of all, a Soviet ring had been operating within the Manhattan Project itself. While only a small number of the uncovered spies were Jewish, the most prominent of those identified were including a number working in the Project.
With Ben Gurion's "Israel" exposing policies which looked vaguely communist to the man in the street, with China lost to communism, and with communist spies who also happened to be Jewish passing US atomic secrets to the Soviets, Truman's need to look strong on communism ran head on into an early US recognition of an independent Jewish state and containment was more important than "Israel".
OOC: I've mixed two broad PODs here. First, Having China "lost" earlier puts Truman in a tougher position with a very tough Presidential election in the wings. Second, letting Hoover in on the Venona decrypt project earlier means there's a chance the information developed by the project is used both earlier and more often, which would also put Truman in a tougher position.
Of course, knowing Harry, he still might say the hell with it all and recognize Israel on schedule anyway!