One piece of evidence for this observation comes from its occurence in a book written in the Eastern Jin Dynasty (317–420). Faxian (or Fa-Hien, Fa-hsien) (337–c. 422) "was a Chinese Buddhist monk who travelled by foot all the way from China to India, visiting many sacred Buddhist sites." His 《佛国记》 (Record of Buddhistic Kingdoms) (a.k.a 《法显传》, Biography of Faxian) states that "从是以南，名为中国。中国寒暑调和，无霜、雪。人民殷乐无户籍官法。" (The place from here toward the south is named the Middle Country. In the Middle Country, cold and heat are harmonized, and there's no frost or snow. The people are well-to-do and happy. Household registry or government laws do not exist.)
Why does Faxian's book serve as evidence for lack of the affective sense of "中国" in early China? The word "中国" first occurred in the ealiest book in Chinese history, 《尚书》 (Book of Documents)[note], which was compiled by Confucious (551–479 BC) and read and memorized by every pupil that could afford minimum education in ancient China. Monk Faxian definitely knew most if not all words in the book. But he used the word "中国" to denote the central area of today's Indian subcontinent, to be precise, to translate the Sanscrit word "Madhya-Des", paraphrased as "central territory" or "central kingdom" or "midland country" by various scholars, which existed during the Gupta period (approximately 320 to 550 CE). It's hard-pressed to imagine that Faxian would have chosen "中国" if it had already had acquired a sense beyond its literal meaning. If "中国" had been used dearly as words such as "夏" or later in history "大唐", Faxian would have considered a different character combination to translate the Sanscrit word, or perhaps added a translator's note if "中国" had to be used.
More than a millenium later, 《四库全书总目》 (Annotated Catalog of the Complete Imperial Library, completed in 1798 by the Qing dynasty) criticized Faxian's word choice by saying that he "以天竺为中国，以中国为边地" ("considered India as the Middle Country and China as the frontier"; note the same word "中国" could mean both "Middle Country" and "China"). What we can read off of this critique is that the word "中国" had acquired its affective sense by the late 18th century. From now on, it's not to be used to mean just the middle part of some part of land, or any country in the middle of something larger. It uniquely refers to the Middle Country or the Middle Kingdom, with its rich culture and history. Yet two centuries later, it's our turn to criticize the editors of the imperial encyclopedia for their lack of the sense that one born later in history should only judge a historical figure from the historically contemporary perspective.
[note] 《尚书·卷十四·梓材》: "皇天既付中国民，越厥疆土，于先王肆" (The heaven already obliged [the Zhou family] to govern the people in the Middle Country. If we extend and develop the territory, our ancestor's Dao will flourish.)