The notion that the Great Wall contains human bodies is an interesting one, and goes in some unexpected directions.

First, because it bears mentioning, when we use the phrase 'Great Wall' we are potentially referring to two separate concepts. The first is the rather clumsy colloquial use of the term to describe every frontier wall built by a Sinitic state (plus also the Mongolic Khitan Liao and the Tungusic Jurchen Jin), much though not all of which are now eroded beyond recognition; the second is specifically the largely-extant wall built in stages by the Ming between about 1470 and 1570. The issue is that there is a tendency to compress all of these into a single entity, but as I go into in this answer, even if we do use the phrase 'Great Wall' we need to understand that there have been many 'Great Walls', both geographically and chronologically discontinuous. So, in turn, there was not simply a construction of the Great Wall, because there have been many constructions, and the tale about human remains refers to the Qin walls of the late 3rd century BCE, and not the extant Ming walls of the 15th and 16th centuries CE.

Under the Han, the walls built by the Qin were portrayed as symbolic of the tyrannical impulses of Qin Shi Huang and his exercise of Legalist philosophy, which in its political form advocated for absolutism and the ultimate power of the state, embodied in the person of the emperor. Per Arthur Waldron, this found its way into two parallel discursive traditions, one elite and one popular, around the construction of the Qin frontier walls. The elite tradition centred on the imperial court, where, according to the Han court historian Sima Qian, Qin Shi Huang's right-hand man, Meng Tian, was made to commit suicide after the emperor's death in 210 directly due to the wall construction. In the brief monologue Sima Qian has Meng Tian deliver before taking the fatal poison, he states that in building ramparts from Lintao to Liaodong, he must have cut across the veins of the earth, this being his capital crime. Sima Qian himself, however, regarded Meng Tian's principal crime as his repeated conscription of labour and callous disregard for public welfare, but even then that was intimately tied with the massive mobilisation of labour towards wall construction.

The popular vein focussed on how wall-building affected the local populace on a much more intimate level. Folk songs around the Qin walls became commonplace, with one song warning parents to abandon sons at birth as they would only end up suffering and dying as conscripted labour at the foot of the wall, and to celebrate the birth of daughters instead. This verse would be incorporated into a number of later ballads by elite writers. But it is important to note that the bodies lay outside the wall, not in it, in this telling.

The story of bodies being in the wall relates to the legend of Lady Meng Jiang, a pretty famous tale in Chinese folklore, and one with a complex history. Its earliest form comes in a 4rd century BCE text, the Zuo zhuan (or Commentary of Zuo), which, yes, predates the Qin-era wall constructions. It is also incredibly brief, and consists solely of the statement that the anonymous widow of Qi Liang insisted that ritual propriety be observed by the state that had sent him to war. The connection with a wall – of any sort – was added by the Han scholar Liu Xiang ca. 18 BCE in the Lienü zhuan (Biographies of Exemplary Women), who states that she wept over her husband's corpse at the foot of the city wall, which collapsed ten days later. Note that this was merely the wall of her city, not a frontier wall. Folk narratives around bodies being buried in frontier walls emerged during the Northern and Southern period (typically defined as 420-589 CE but some have stretched the term back to begin with the Three Kingdoms period starting in 220), when fortification was especially prolific and mortality was high. Only during the Tang period (618-907) do we see the older legend of Lady Meng Jiang (who also only began going by this name around this time) merge with much later motifs of mortality in building frontier walls, to produce the modern folk tale in which it was the Qin wall specifically that actually contained human bodies.

As an aside, it is worth stressing, as u/itsallfolklore is wont to do, that the notion that folklore must contain a grain of truth is itself folklore. When I (well, technically Arthur Waldron as summarised by me) say that stories circulated about bodies buried in frontier walls, that does not mean that there were bodies, only that there were stories. We cannot definitively disprove that there may have been, but even if so the folk tales would be correct only by coincidence.

The chronological compression of Great Walls is not a novel development, and indeed even the Ming walls, soon after they were built, found parts of the Meng Jiang myth projected on them. In the late 15th century, the fortifications at Shanhaiguan were alleged to have originally been built by the Qin and restored by the Ming (they were not; the Qin frontier was further north), and to have been where Meng Jiang found her husband, and one of the towers was dubbed the 'husband-watching-tower' as being the place from which she tried to spot him in the crowd. A shrine to Meng Jiang would be established (or possibly re-established) in the area in 1594, tying the Tang myth around the Qin wall into the Ming wall of the then-present.

For further reading, the definitive treatment of the Great Wall in English remains Arthur Waldron's The Great Wall of China: From History to Myth (1989).

I will follow up with u/EnclavedMicrostate 's answer by unpacking the interesting historical evolution of the "dead bodies of workers/soldiers within the Great Wall" narrative.

At its core, "dead bodies within the Great Wall" can be better understood as a poetic expression within the history of Chinese literary tradition rather than something based on factual events. Given what is known about the construction method of Qin era defensive walls, even IF (and that's a big "if," more on this later) involved excessive death and suffering, it is both highly unlikely and counterproductive to bury bead laborers beneath the Wall.

In fact, we don't actually know for sure whether or not the construction of the Qin Great Wall involved an unusually high number of dead conscript laborers, and more recent research in this area increasingly challenges this long held assumption. The historical symbolism of the Great Wall as a material manifestation of Qin dynasty's brutal rule initially emerged from official historical records of Han dynasty, most notably in The Book of Han. [1] [2] Keep in mind that Han dynasty proclaimed its imperial legitimacy (or Heaven's Mandate) through the narrative that it overthrew the tyrannical rule of its predecessor Qin, and therefore it is reasonable to assume that the Han Course has a political interest for painting major Qin construction projects (most notably the Great Wall and Epang Palace) under a negative light.

The vast majority of workers involved in the construction of the Qin Great Wall are regular conscript laborers. I have previously discussed the institution of conscript labor during early imperial China in here and here, feel free to take a look. Both Qin and Han dynasties operated similar kinds of conscript labor systems which originated from the Warring States period. Contrary to popular belief, those conscripted laborers were paid per diem, and provided with housing arrangements and daily food rations.[3] Building long fortification walls using conscript labor has been common practice throughout China both before AND after Qin dynasty, and we have no concrete evidence suggesting that Qin’s Great Wall project was unusually brutal when compared to other periods.

While Han historical records framed the Qin Great Wall as an excessive, costly, and burdensome imperial vanity project, it did not mention anything relating to “bodies buried beneath the Qin Great Wall.” The earliest of such narrative emerged from literary rather than historical sources, specific in the poem 《飲馬長城窟行》by late-Han poet and a key figure of the Jian'an literary movement Chen Lin, when he used the expression “君獨不見長城下，死人骸骨相撐拄 (He who seeth not undeath the Great Wall, bones of the dead form its scaffolding)” as a metaphor for the human toll inflicted by continuous warfare right around the Three Kingdoms period when he wrote this poem. [4]

This poetic expression further evolved during another tumultuous time of Chinese history known as Five Dynasties and Ten Kingdoms period, most notably in a poem by late-Tang poet buddhist monk Guan Xiu (832 - 912) known as 《杞梁妻》or Madame Qiliang.[5] This poem presents a dramatistic re-telling of the well-known historical figure Madame Qiliang (? - 550 BC) from the Spring and Autumn period. Except instead of committing suicide after the tragic death her husband Qiliang, a Qi commander who was captured by the rival state Ju and was executed for refusing surrender, our poet Guan Xiu transplanted this well-known historical figure into the context of Qin Shihuang’s construction of the Great Wall. In the poem, Madame Qiliang was “reincarnated” as a wife of a common Qin conscript who died from building Shi Huangdi's Great Wall. And this poem became the prototype of a literary motif fusing the “Bones of the Dead Supporting the Great Wall” expression and the tragic tale Madame Qiliang, and eventually further evolving during late-Yuan/ early-Ming dynasty into the popular folk legend Meng Jiangnu as already discussed by u/EnclavedMicrostate [6]

TL/DR: "Dead bodies of workers/soldiers within the Great Wall" was more of a fiction than fact, but it persisted as an important poetic expression for human suffering under tyrannical rulers in China.

Sources: [1]漢書 -> 傳 -> 武五子傳 -> 44 秦始皇即位三十九年，內平六國，外攘四夷，死人如亂麻，暴骨長城之下，頭盧相屬於道，不一日而無兵。 [2]前漢紀 -> 高祖皇帝紀一 -> 3 秦為亂政虐刑。殘賊天下。北有長城之役。南有五嶺之戍。內外搔動。百姓罷弊。財匱力盡。重以苛法。使天下父子不相聊生。 [3]《云梦睡虎地秦简》有罪以貲贖及有責於公 以其令日問之 其弗能入及賞 以令日居之 日居八錢 公食者 日居六錢 [4] 魏晉：陳琳 《飲馬長城窟行》（？－217年） https://www.arteducation.com.tw/shiwenv_bfd9010d755d.html [5] 貫休 （832年－912年）的詩《杞梁妻》:秦之無道兮四海枯，筑長城兮遮北胡。筑人筑土一萬里，杞梁貞婦啼嗚嗚。上無父兮中無夫，下無子兮孤復孤。一號城崩塞色苦，再號杞梁骨出土。疲魂饑魄相逐歸，陌上少年莫相非。 [6] 顧頡剛《孟姜女故事研究》