The golden age of being optimistic about the future can be bookended by the 1939 and 1964 World's Fairs. Both were held in New York City and both lasted two seasons. Both Fairs attracted large crowds and showed many fantastic new products to the American consumer. However, by 1965 the "future" was starting to look kind of old. The United States was facing more serious social problems, like the war on poverty, civil rights, women's liberation, the Vietnam War and environmental problems. After 1965, the US was less optimistic about the future than it was during the 1950s.
Source: "Populuxe: A look at life of America in the '50s and '60s, from tailfins and TV dinners to Barbie dolls and fall-out shelters" by Thomas Hine.

In 1900, cars were a new technology. Airplanes came shortly afterward. After world war 2, humans launched spacecraft, and were on the cusp of personally travelling to outer space.

A person of that era could reasonably have expected this technological explosion to extend to their personal life, making flight accessible to the common person.

Our technological trajectory was not particularly obvious. If you're interested in this idea, I recommend getting your hands on some science fiction from the middle of the 20th century. Arthur C. Clark is a great place to start, in my opinion.

The 50's were a very optimistic time for America at least especially. They had recently won World War 2 and were now in the midst of a cold war with the Soviet Union. This meant that there was still lots of military research going on, which influenced the public's view of what the future would hold.

In many ways this is about the new but flawed understanding about nuclear energy, theoretical physics and material science. The jetpack is limited practically by energy density of the fuel. A man portable device might give you 60 seconds of flight at ~1G of acceleration. Neat, but not a solution to the work commute. Nuclear fuel could offer energy density orders of magnitude greater which prompted people to assume that limiting elements of current engineering problems would be solved without understanding that the new solutions required new engineering challenges which created new problems for realizing these foundational dreams. So yeah, nuclear decay in critical reactors is amazingly energy dense compared to burning bunker fuel or natural gas but you need a giant industrial facility to turn that heat into mechanical energy through turbines, subsequently into electrical energy to distribute to all the folks out there. None of which makes a jetpack even remotely practical.