They start targeting possible recruits as early as middle school and high school. There is a sort of "boy scout" type organization for geeky pre-adolescent kids and adolescents--mostly boys--who are fascinated by computers, programming and possibly hacking. By the time a kid hits draft age, he or she is already a known quantity. This vetting program sorts out not only the talented, but those who may have an inclination to be politically unreliable, along the lines of the infamous traitor Vannunu, who gave away many of their atomic secrets. Remember, Israel has a dense population in a small land so its easy to find someone who "knows the family".  

The program started because their government computers were hacked by their own under age citizens. Remembering the adage "idle hands make mischief", it was thought wise to redirect this energy into useful purposes. By the time a kid in this program is drafted, he/she will already be much more knowledgeable about programing than most American or Commonwealth kids can learn without guidance. 

This level of talent is rather similar to young people at the highest caliber of athletics or musical accomplishment.  A kid who receives this training only in university may become good, but will probably not be quite good enough for what the Israelis do on the field of cyber warfare.  America of course has the advantage of having a large population base from which to choose, so by virtue of numbers might be able to compensate for her traditional lack of rigor in the early and middle school levels of education.

With respect to the suggestion of the previous poster, I believe that the intellectual edge of the best of these people is not financial motivation. It is the belief that one is intellectually superior to the competitor (in this case a foreign enemy) and that one can, through guile and stealth, outwit them.  Everything else is secondary. There will be limits to purely financial motivation.