Frederik Pohl had a story in which the US developed a Typhus Bomb--the US spread typhus through Japan. So medical science was developed more, and the atomic bomb was never developed, so there was no nuclear fears, no fear of science, sf had a better reputation; Entertainment Tonight covers all the sf conventions in that timeline, and sf writers are often on various talk shows and different magazines.
Tesla marries into a wealthy family, who funds his research.
Stalin is overthrown and the USSR collapses at the end of WW II, with no Cold War, the military doesn't dominate NASA's planning, the space shuttle is never developed. But there's rivalry with the new military government of the USSR, but not the Cold War and Red Scare, so the space program starts earlier.
Heinlein's story "The Man Who Sold the Moon" was about a private entrepreneur and his own space program.
Harry Turtledove had a story, or novel, in which one member of a starship crew had the specialty of being familiar with many different sf works. So whenever they enounter a situation in space, she can compare it to some sf story's situation and come up with a solution to the problem.
So on one particular mission, they encounter a situation on a planet and she uses an idea from Heinlein's story to solve the problem.
Goddard teams up with Tesla and Einstein, and maybe the Rockefellers to start their own rocketry program.
The Depression is avoided but WW II takes place anyway; with a better economy, would corporate research and development have been more advanced?
NASA is established at the end of WW II, with or without the dominance of the military.
The British start their own version of NASA at the end of WW II.
Arthur C. Clarke came up with the idea of the telecommunications satellite during the 40s but didn't think of patenting it. That deserves its own thread....