To answer this question, I am expanding "moon landing" not to mean "when did people begin to tackle, seriously, the technical problems of an Earth-Moon journey" and rather to answer, "when did they begin to hypothesize such a thing."

I am drawing from a succinct article called "Early Modern Space Travel and the English Man in the Moon" (David Cressy. The American Historical Review, Vol. 1, No. 4, October 2006), as well as my own research. I almost wrote on this topic for my thesis, but ended up getting diverted into something less well written about.

In his article, Cressy talks about numerous pre-Early Modern speculators of a philosophical or religious bent--positing multiple words with multiple inhabitants. For example, William of Vorilong (1390-1463). According to Cressy, for Christians, this was part of a discussion about sin and redemption. Would otherworldly people have sinned? Would they have been redeemed? However, this is clearly a different kind of discussion of multiple worlds.

Galileo Galilei is famous for being the person to identify, using a telescope, that the moon was a rocky object much like the Earth. This was 1609. However, a year earlier, Johannes Kepler had written the Somnium, which imagined a Earth-Moon journey. The Somnium, however, was modified over time to have more of a narrative and wasn't published until the 1630s, which was incidentally when Earth-Moon stories were taking off.

From Cressy again: "A series of publications in the late 1630s put the moon and its inhabitants, and the likelihood of traveling to meet them, into the national conversation. The key texts...were John Wilkins, "The Discovery of a World in the Moone" (1638) ... Francis Godwin, "The Man in the Moone" (1638)... and Wilkin's revised and expanded edition of A Discourse Concerning a New World & Another Planet (1640)." These imagined trips to the moon, inhabitants.

Later in the 17th century, other people imagined a rocky world, perhaps one that could be traveled to. For example, Pierre Borel, from France. Borel's book was published in France in 1657 and translated into English the following year (which suggests it was popular). He wrote--like Kepler before him--with a fascination of what the Earth would look like, or seem like, or behave like, from the surface of the Moon.

ALL Philosophers and Astrologers are agreed, That the Earth and Moon have this commune between them, that they both are thick, grosse, dark, and solid bodies, able to receive and refresh the light of the Sun; this being granted, What is easier than to conclude, That the Earth reverberating the beams of the Sun, would appear lightsome to them who should be raised high towards Heaven? that it would seem so little and small by its far distance from us, that it would be almost like the Moon, both in light and bignesse; and that it would even have its spots, because of the waters which bury and smother the Sun beams; and do not reverberate them.

Borel also proposes residents of the Moon, speculating on how they might survive there (and using contemporary exploration as an example):

BUT some may say, There cannot be such Men as we, in the Starres; for they could not live there, because men are divers, even after the diversity of Countreys; and those who ascend that high Mount Piracaca in the Indies, dye there by reason of the too subtile ayr of the place. To which I answer, That those men must needs be different from us, or imbued with more robust and strong bodies then we; or so well proportioned in the mixture of the Elements, that that Ayr cannot be obnoxious and hurtful to them; but that God hath so formed them, that they may well live where he hath placed them, but no where else.

Interest continues towards the end of the 17th Century. Bernard de Fontenelle's "Discourse on the Plurality of Worlds" was published in 1686 in French and translated a couple of years later by Aphra Behn, among others. Interestingly, Behn in 1687 published a play called the Emperor of the Moon which went to someway to mock some of the earlier moon-journey stories like those by Godwin and Wilkins. However, clearly she, along with Fontenelle had a keen interest in the moon as another world, if perhaps not stories about being transported there by geese.

Fontenelle's book is a kind of introductory science book in which various topics--including inhabitants of the moon--are explained to a woman, a Marchioness. The Marchioness asks questions and is given answers. A lot of the conversations centers around Men in the Moon, and some thought is given to the possibility of travel to them:

Oh! says she, I reckon the Inhabitants of the Terra Australis as known; for 'tis certain they must needs resemble us very much, and in fine, we may know them when ever we take the pains to go see them, there they are and cannot avoid us; but the people of the Moon, we shall never know, 'tis that I despair of.

If I should answer you seriously, said I, that we know not what may come to pass, you would laugh at me, and I should well deserve it, but in the mean time I could defend my self well enough if I pleas'd. I have a thought in my head that is very ridiculous, which yet (I know not how I got it, being so imper|tinent as it is) has some appearance of truth. I'le hold a Wager, that I'le bring you to acknowledge against all reason, that there may be in time a Commerce between the Moon and the Earth. Consider with your self the Circumstances of America, before it was discover'd by Christopher Columbus, the Inhabitants lived in the extremest Ignorance, so great strangers to knowledge, that they knew not the most simple and most necessary Arts, they went naked, had no Arms but the Bow, and could never imagine that Men could be carried by Animals; they look'd upon the Sea as a great space prohibited to Men, that it was joyn'd to the Heavens, and that beyond it was nothing.

'Tis true, after spending whole years in making hollow the Trunk of a great Tree with sharp stones, they put to Sea in that Trunk, and coasted the Shoar with Wind and Tide; but as that Vessel was often subject to overset they were as often put to swim to recover it; and, to speak properly, they constantly swam, only then when they took breath in their Boats. Whoever should have told them that there was another sort of Navigation incomparably more perfect, that men could traverse that vast extent of Waters where and how they pleas'd, that they could stop without motion in the midst of the rolling Waves, and command the swiftness of their Course; and in fine, that the Sea, vast as it is, was no obstacle to the Communication of people, provided there were people on the other side, you may well imagine they would never have believ'd it.

Yet you see the time came, that the strangest Spectacle in the World, and the least expected by them, appear'd before them, huge enormous Bodies that seem'd to fly upon Sea with white Wings that vomited fire on all sides, and cast upon their Shoars an unknown sort of people clad with Iron, governing those Monsters that ran upon the Sea, as they pleas'd, and bearing Thunder in their Hands that beat down all before them. From whence come they? Who could bring them over Sea? Who put the Fire in their power? Are they Gods? Are they Children of the Sun? For certainly these are not Men. I know not, Madam, whether you conceive, as I do, the great surprize of the Americans, but certainly never any equall'd it.

After all this, I will no more swear that there will not be in time a Commerce between the Moon & the Earth. Could the Americans believe that ever there should be any between America and Europe, and that they alone should not know it? 'Tis true, there is a great space of of Air and Heaven to be travers'd between the Earth and the Moon, but did those great Seas appear to the Americans any more fit for passage?

Men begin already to fly a little, several persons have found the secret of fi[...]ting themselves with Wings, that support and give them motion in the Air, and they can fly over Rivers, and from Steeple to Steeple. 'Tis true, 'tis not the flight of an Eagle, and it has cost those new Birds sometimes a Leg or an Arm; but that in the mean time does but represent the first Planks that were set a sloat, and were the beginning of Navi|gation. There was a great distance or difference between those Planks and a great Ship that could make a Circuit about the World, yet by little and little they are grown up to a great Ship. So the Art of Flying is yet in its infancy; it will daily grow towards perfection, and sometime or other we shall get up to the Moon...

I think here you have your answer. In the 17th century, the invention of the telescope and its use in discovering the mountains and valleys of the moon, coupled with the ongoing Earth exploration, allowed the exciting realisation that the Moon might be a physically visitable place (as opposed to a philosophically visitable one) and--for Fontenelle at least--real travel there only a matter of time and technology.