What elements led the growth of suburbia?

I would say that the end of World War II, with the benefits afforded to returning GIs, the post-war baby boom, the investment in interstate highways, a housing shortage, and the resumption of production of the automobile were major factors in the development of suburbia. 

When World War II was over, thousands upon thousands of soldiers returned home, and when they did so, they were afforded benefits such as college education and easy to obtain, low-interest housing loans.  Because many of these GIs had delayed marriage and/or having children because of the war, when they returned home, they began reproducing to the point where their offspring became the largest generation in American history, the baby boomers.  As they began to marry, have children, and acquire educations, they had available government or government-guaranteed housing loans, with very little money needed for down payment and very favorable interest rates. Since there was very little residential construction during the war, a housing shortage had built up, and so, most GIs were in need of new houses. (My own parents lived in a one-room apartment when they married right after the war because of the housing shortage.) Moving out just a bit from the cities, the land was cheaper, and there were plenty of companies breaking ground in new developments. Levittown is often cited as the perfect example of this phenomenon, a new suburb built to deal with the pent-up demand of returning GIs, with their brides, their children, and their wherewithal to get mortgages. 

Simultaneously, automobiles, which had not been manufactured at all during the war because all manufacturing was directed toward the war effort, began to be produced once again.  Returning GIs, with their better jobs, thanks to their education, and their families, were more than ready to buy them now.  And the interstate highway system, begun in the interests of national defense, really began to take off.  This meant that people now had cars to drive and good roads to drive them on, beyond the streets and avenues of the cities or the two-lane country roads.  Commuting from a suburb became something that was manageable with new cars and better roads.

All of these elements combined into a situation that was ideal for the explosion of suburbia post-World War II.  This trend, which I would guess peaked some time in the 70s or 80s, is now being reversed, with movement in two different directions, those who are moving more to the cities and those who are running off to live a rural life. The pendulum is always swinging!