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.