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Safe human travel into space had to have become scientifically accepted as plausible long before any nations managed to successfully pull it off (and unsafe or one-way human travel likely earlier than that), but I'm having trouble finding any documentation of scientific discussion of the concept in terms of when it went from being considered as "probably impossible" or "currently unknown" to "probably possible in the future".

I've found that the idea using rockets to reach space was conceptualized in the 19th century and the early 20th century by scientists such as William Leitch, Konstantin Tsiolkovsky, and others, but I'm unsure how seriously these were taken by the scientific communities at the time, or if it was thought possible earlier, just without knowing a plausible mechanism to do so yet.

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    $\begingroup$ It always helps to remember May's quip:"If we describe a result with sufficient vagueness, there seems to be an endless sequence of those who had something within the vague specifications". You won't be able to draw any meaningful lines with something as vague as "scientifically accepted". See Nature, Moon on the mind for one timeline. I'd highlight Vernes's From the Earth to the Moon (1865) that involved some calculations and made the idea mainstream, but it was just incremental slog. $\endgroup$
    – Conifold
    Sep 28, 2021 at 20:59
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    $\begingroup$ Outside my expertise thus not an answer. I'd say this happened in the 1920s based on earlier work by Tsiolkovsky and others. Publications: Hermann Oberth, "Die Rakete zu den Planetenräumen." München: R. Oldenbourg 1923. Walter Hohmann, "Die Erreichbarkeit der Himmelskörper." München: R. Oldenbourg 1925. Hermann Oberth, "Wege zur Raumschiffahrt." München: R. Oldenbourg 1929. Verein für Raumschiffahrt (Society for Space Travel) was founded in 1927. Fritz Lang's film "Frau im Mond" 1929 (which supposedly introduced the concept of launch countdown), with Oberth as technical adviser. $\endgroup$
    – njuffa
    Sep 29, 2021 at 23:09
  • $\begingroup$ A popular science publication from the 1920s: Max Valier, "Der Vorstoß in den Weltenraum", München: R. Oldenbourg 1924 $\endgroup$
    – njuffa
    Sep 30, 2021 at 3:00

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From the Russian Wikipedia article (my translation): Perhaps the first person who pointed to the possibility of using rockets for travel in space was W. Leitch. In 1861 he wrote an article "A Journey Through Space" which was published in 1862 in his book "God’s Glory in the Heavens".

In 1881, Kibaltchich, while imprisoned [for revolutionary activity], put up an idea of a flying apparatus with jet propulsion. A few days before his execution, Kibaltchich developed a detailed project of such an apparatus for space travel. It was published only in 1918.

First person who studied theoretical aspects of space travel was Tsiolkovsky who developed, in particular, the Tsiolkovsy formula (that, in particular, formed the basis of Soviet space program).

A little later, German scientist H. Obert also found, in 1923, the main equation of the rocket technology and showed that using multi-stage rocket (as suggested by Tsiolkovsky) one can move an arbitrary large object into a desired orbit.

The English Wikipedia article about Tsiolkovsky includes a part about his influence on the scientists who made actual rockets for space travel (von Braun, Korolev, others):

Although many called his ideas impractical, Tsiolkovsky influenced later rocket scientists throughout Europe, like Wernher von Braun. Soviet search teams at Peenemünde found a German translation of a book by Tsiolkovsky of which "almost every page...was embellished by von Braun's comments and notes."  Leading Soviet rocket-engine designer Valentin Glushko and rocket designer Sergey Korolev studied Tsiolkovsky's works as youths, and both sought to turn Tsiolkovsky's theories into reality.In particular, Korolev saw traveling to Mars as the more important priority, until in 1964 he decided to compete with the American Project Apollo for the Moon.

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Among the early proponents of space travel, a Ukrainian engineer Yuri Vasilievich Kondratyuk should be mentioned. In 1925 he published his book Conquest of Interplanetary Space with theoretical justification of space travel. His research could not continue since he was arrested and imprisoned by the Spoviet authorities. But his book made an influence of the later developers, and his contribution is well recognized: for example a crater on the Moon and an asteroid are named after him. His ideas were used in planning of Apollo missions.

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