Oh it was definitely noticed, probably widely so as well. I'll just address the two types of people who would have been in direct contact with the Ming and Qing during the transition: The merchants from trading powers (Spain, Portugal, Dutch) and Missionaries, both religious and diplomatic.
Starting with the mid-Ming, probably around the time of the Wanli reign, European missionaries began to arrive to China in force, and most of these men were Jesuits. At the same time, and really long before the missionaries, European trading powers like the Portuguese had established trading relations with the Ming dynasty. There are many accounts of European interactions with the Ming, as evidenced by the wide body of written work produced by Europeans as they worked to establish Catholicism in the Chinese empire. Matteo Ricci is probably one of the most well-known of these Jesuit missionaries, but he was merely one of many.
I'll start with the literary works of the European missionaries. Father Martino Martini (sick name) was a Jesuit of Italian origin, sent on a mission to China in the mid-17th century. He arrived in Macau in 1643, which at the time had been used by the Portuguese as a trading base with China for around a century. But by the time of his arrival, the fall of the Ming was already imminent, and the Ming government was in full-on panic mode. Peasant rebellions, including two notable ones led by Li Zichen and Zhang Xianzhong had pushed the Ming into a perilous situation, and governmental neglect of public works had resulted in repeated flooding of the Yellow River, widespread famine that was exacerbated by the Little Ice Age, and the breakdown of central military authority meant that bands of roving soldiers, trained and armed to kill peasant rebels, were instead roaming the countryside killing the peasants they were meant to protect in order to survive themselves.
Martini traveled to Southern China, and within three years of his arrival and establishment of a Christian ministry in Hangzhou, was a witness to, both directly and indirectly, the capture of Beijing by Li Zichen, the suicide of the Chongzhen emperor, and the establishment of Nanjing as the new capital of the rump court known as the Southern Ming. He wrote a number of books detailing his experiences and the events that transcended while he was in China, including Da bello Tartarico, which detailed the turbulent conflict between the Manchu 'Tartars' and the Chinese Ming. He returned to Europe briefly in 1651, which is when he presumably published his writings, and they rather quickly disseminated throughout the continent. I say this because in 1654, an Englishman named John Crook translated and published English versions of his work, and so I can only presume that his writings also spread to literate circles in other European countries.
The Dutch East India Company sent a Johann Nieuhof just after the fall of the Ming, sometime during the early 1650s to promote trading interests for the Dutch, and it seems as though they were fully aware that a governmental transition had occurred. One of the reasons that the Dutch ambassadorial mission was sent was because the Manchu rulers seemed to offer a new hope for expanded or changed foreign relations between China and the West (in the European's eyes anyways), so clearly there must have been some degree of awareness going on here that the Ming had fallen. There were also additional interactions following the fall of the Ming, such as when the Southern Ming fled to Taiwan, which resulted in the Dutch loss of the island. As a last note, in 1665, the Dutch East India Company published the A Legation of the Netherlands East India Company to the Greater Tartar Khan, now Emperor of China, which was widely circulated throughout Europe, further indicating awareness of this dynastic shift.
Sources:
Struve, Lynn. Voices from the Ming-Qing Catacylsm: China in Tiger's Jaws. Yale University Press. 1993.
Cambridge History of China, Volumes 7 and 8. Cambridge University Press. 2008.
Mungello, D. The Great Encounter of China and the West: 1500-1800. Rowman and Littlefield Publishers. 2012