Source of Chinese textbooks from the second to last paragraph here
How can you really know?
The short answer is that the outbreak of the war and the invasion by North Korea are extremely well documented. And this set of facts rests on documentary and testamentary evidence from Russia, US, South Korea, and Chinese Sources. The international academic consensus also overwhelmingly accepts this set of facts. Though the North Korean and Chinese governments endorse official histories which are at odds in whole or part with this consensus.
Looking at the evidence itself
However, if someone is inclined to dismiss this mass of scholarship and evidence as a global conspiracy. The argument becomes a bit more difficult.
I think the most straightforward line of alternative argument is that war broke out when the South Korean military was unprepared for war. At a time when US military strength in the ‘Far East Command’ was likewise extremely low and mostly unprepared for war.
US force levels were steadily reduced from the end of WWII. In 1947 MacArthur commanded over 300,000 troops in the Far East Command, but by June 1950 this had dwindled to only 108,500 army troops. Shrinking troop levels were accompanied by a near total lack of investment in material and weapons. Army postwar procurement was almost entirely limited to “food, clothing, and medical supplies” with the army expected to rely on aging stocks of leftover WWII weapons.
MacArthur in 1947 had commenced ‘Operation Roll-Up’ to refurbish US equipment which had been left to rot at bases all around the Pacific when the war ended. This did lay the groundwork for the repair and production of military equipment in Japanese factories. But the program was not complete by the deadline of June 30, 1950. At which point “an estimated 80% of the army’s 60-day reserve of armament equipment was unserviceable.”
Far East command received no new vehicles, tanks, or other equipment between the end of WWII and the outbreak of the Korean War. Crucial equipment, everything from recoilless rifles to heavy trucks, were present in low numbers and 50-90% of stocks were unserviceable.
The South Korean military had no tanks and “virtually no air force”. In contrast to North Korea's 150 medium tanks and small tactical air force. The North had a 3:1 advantage in artillery and tens of thousands of experienced troops who had fought in the Chinese Civil War. South Korea also failed to make any preparation for defense in depth or a layered supply system. There were no plans for a fighting retreat or destruction of supplies in the event of a retreat. Accordingly, once the invasion occurred South Korean military supply and communication broke down in the early stages of the war.
The specific disposition of South Korean forces when war broke was also highly disadvantageous. Units were under-strength due to farming season furlough. Even more soldiers and officers departed for the weekend because an existing alert order was lifted. Huge numbers of officers were away from their posts in Seoul sleeping off the effects of a celebratory banquet. Others were abroad in the US or Japan. The head of the US advisory group in Korea had been reassigned and his temporary replacement was in Japan. Of the four divisions posted on the border, only four regiments and one battalion were actually stationed on the line. This utter unpreparedness is seen in the disastrous retreat of South Korean forces south. Or in incidents such as the premature destruction by S. Korean forces of the bridge on the Han River which trapped several friendly units on the other side.
It should be noted that there is ambiguity over who shot first the morning of the invasion. There had been sporadic violence and skirmishes on the border for many months, and it is possible that S Korea launched small raids or artillery strikes that morning. But these attacks which had been occurring for months were met with a North Korean invasion involving amphibious landings, air attacks, and thousands of troops across a broad front. North Korean troops who had been moved to unprecedented concentration on the border over the course of weeks and months.
I suppose it is possible to throw out all the diplomatic evidence and argue that the North Koreans concentrated their entire forces in an aggressive stance but weren’t actually intending to invade. And then argue even less plausibly that they were tricked/provoked into a massive invasion by some small South Korean cross-border raid. But I do not find this line of argument very convincing. Amphibious landings like North Korea conducted are not spur-of-the-moment endeavors. It also requires ignoring the mass of evidence for North Korea’s diplomatic preparations for the invasion.
When war broke out, South Korea was still struggling to suppress an armed guerilla movement, and their military forces were much more oriented towards counterinsurgency than conventional warfare. The idea that South Korea or the US would intend for war or try to provoke a full war at a time of such unpreparedness strains credulity.
There is overwhelming evidence and consensus that North Korea planned the war and invasion long in advance, closely coordinating with China and the USSR. But even if one dismisses this evidence, the idea that South Korea or the US would choose to invade or try to provoke a war in the summer of 1950 is absurd.
Sources:
[edited to fix typos and improve clarity on certain points]
One of the best ways to ascertain 'truth', insofar as it can actually be known, is to rely on primary source documents. While a document is not necessarily truthful simply because it exists, the context in which the document was made or found can give a strong indication of how reliable it is. For example the minutes taken of a meeting among government officials that was never intended for public release could be considered fairly accurate. While a government press release trumpeting the latest victories in a war effort may need to be viewed through a more critical lens.
For the Korean war, a wealth of documentation became available to historians with the fall of the Soviet Union in 1991. It became possible to access the Russian archives which greatly expanded our knowledge of the inner workings of the Soviet Union through various points in history. Regarding your question specifically, this meant a wealth of documents and cables regarding the Soviet leadership's correspondence regarding North Korea prior to the invasion. These discussions and messages are primary source documents that show the thinking, discussions, and analyses for key players in the period prior to the war. These include the direct correspondence between Stalin, Kim Il Sung and Mao Zedong specifically regarding Kim Il Sung's intent for an aggressive war against the Republic of Korea.
A useful archive of these documents can be found at the following link. Many documents can be viewed as scans of the original. https://digitalarchive.wilsoncenter.org/collection/134/korean-war-origins-1945-1950/2
To pick a specific example, the telegram on September 14, 1949 occurs one year prior to the Korean War. It details North Korea's strategy and war preparation in minute detail. There is an English translation, but also a scan of the original document itself. The context in which these documents were obtained (secret documents made accessible after the collapse of the Soviet Union 40 years after the events occurred) lend scholars a high degree of confidence in their authenticity. In the end, whether you believe this to be true is a judgement call that you need to make for yourself after critically viewing all of the available information.
Is there a better source to back up the claim that Chinese textbooks state that the Korean war was started by South Korea as a springboard for US invasion of China?
The article linked makes the claim without any link or evidence to support that claim.
So I went and found this Chinese textbook for high school students:
Volume 2, Teachers' Guide of the Modern History of China.
There were different textbooks by different publishing houses that Chinese schools could choose from, but this one was from People's Education Press which tended to be one of the most popular choices.
After reading the textbook, I didn't find anything to support that claim.
The criticism I would make about the text is that it just says 'the Korean War broke out in June 1950' without clearly stating that it was the North Koreans who invaded South Korea. But, that's not the same thing as the claim the OP is making.