Which incidentally is how most people in antiquity interacted with the works! Festivals would have contests for the recitation of Homer and bards would choose sections that suited their talents, and stories that take place in and around the Trojan War were ripe for adaptation by tragedians (various Iphigenias before the Trojan War, some Ajaxes during and Aeschylus’s Myrmidons took place during the Iliad, and the Orestian cycle after). On top of that people would order only certain books of the Iliad and Odyssey (Iliad II the most popular then and least popular today). Most educated people probably sat down with the entirety of Homer eventually, and many people had it memorized, but most people’s first interactions with the Trojan War myth were piecemeal.

Spoilers are so, so beside the point.

ETA: you mentioned people not reading Homer through all the way. Even if they did they wouldn’t be getting the whole story! The Iliad starts in the ninth year of the war (so no judgment of Paris, no abduction of Helen, no sacrifice of Iphigenia), and takes place over a few weeks and ends with the death and funeral of Hector. Achilles and Ajax deaths and the Trojan horse and fall of Troy all occur offpage between the Iliad and the Odyssey. These were only episodes in a much larger story (and I don’t even think the so-called epic cycle covered all of it).