We’re not talking about all the trouble with heliocentrism. What we started with were Galileo’s problems with heliocentrism, and these really only began with the Dialogue. (What happened to him before was, by comparison, an inconvenience.)
Galileo published Sidereus Nuncius in 1610. This book detailed various observations he made with his new telescope, including Jupiter’s moons, and the problem with it was mainly that while former publications on heliocentrism were careful to present the idea as a mere hypothesis or at best an aid to calculation rather than an explanation of the real world, having actual evidence of heavenly bodies going around heavenly bodies other than the Earth was, on its face, heretical. (His publication on the phases of Venus in 1613, as well as his observations of sun spots, just added to that.) The Church didn’t like the implications of Galileo’s observations but the observations themselves were difficult to argue against (the official astronomers eventually had to concede that there was something to them). As usual, the solution as far as the Church was concerned was to admonish Galileo sternly not to talk or write about his ideas. This is presumably what you mean by “Galileo already being censored before the Dialogue”.
Even so, the cardinal Maffeo Barberini, who became Pope Urban VIII in 1623, had been an admirer of Galileo’s from 1610 or so, and this friendly relationship persisted even after he ascended to the papacy. Urban VIII arranged for Galileo to be allowed to write about Copernicus’s theory again as long as he added the usual precautionary caveats. This arrangement seems to have worked fine until Galileo published the Dialogue in 1632, at which point the Pope was offended and Galileo’s goose was really cooked – the Roman Inquisition tried him in 1633 and put him under house arrest until he died in 1642.
At the same time, the facts were beginning to overtake the various objections that had been made against the heliocentric system. In 1627, Kepler had published his Rudolphine Tables, describing the movement of the planets based on his own theory of elliptic orbits as well as Tycho Brahe’s very exact measurements, and these were far more accurate than anything that existed before. Kepler died in 1630 and Galileo basically had no time for his ideas; even so, Kepler’s writings gained a lot of traction during the following decades, and when Newton published the Principia Mathematica in 1687, including a derivation of Kepler’s laws of planetary motion from his own theory of gravity, the geocentric model was done from a scientific POV whether the Church liked it or not.
