Israel was one of the first countries to recognise The People's Republic of China, after the communist revolution in China. They did so in 1950. This is one year after Mao Zedong declared the establishment of the republic. The USA did not do so until 1978. However, China didn't return Israel's favour until 1992 when they recognised Israel. This is four years after China recognised The State of Palestine. And in fact the PLO had opened a diplomatic office in 1965 which was expanded into a full embassy in 1974.
Given Mao Zedong's view of the communist revolution as a people fighting for their freedom it was only natural that he would view the Israel-Palestine conflict in the same lens: Palestine was fighting for its freedom after Israel was established on their land and bank-rolled by the imperial powers of the British Empire and then the USA.
In Mao's view, it wasn't a question of "undermining Iarael" but of asserting the national rights of the Palestinians which the British had also promised in the Balfour Declaration when they spoke of a "homeland" and not a state to be established in Palestine for the Jews and without "prejudice" to the rights of the Palestinians and others.
It's also worth noting that when the Zionist leadership were offered a homeland in Germany by the British war office once it was realised victory against Nazi Germany was in sight, they refused. They wanted Palestine. This would have made ethical sense in that one of the greatest criminal acts against a people - the Holocaust - was chiefly driven by Nazi Germany. It follows a principle of justice that the perpetrator of a crime pays. And not an innocent bystander. Andvin this case, a far away and inncocent bystander.
However, since China has established diplomatic links with Israel their trade ties have only grown. They are at present the second largest export market for Israel. The first obviously being the US given their strong political ties. Trade volume from Israel to China expanded from $50 million in 1992, when relations were normalised, to $5 billion in 2022.
In fact, this increasing trade - often of military technology - has been of concern to the US. In fact, in 2000 Israel cancelled the sale to China of an early warning system after being pressurised by the US - they threated to cut off their yearly aid, worth $3 billion.
Should one say that Israel "was actively trying to undermine" the USA?
Whilst the economic picture gives the lie to China "actively trying to undermine Israel", the current political stance of China on the Israel-Palestine conflict is one that is both sanctioned by the UN and the USA. That is the two-state solution. Thus it also undermines this accusation.
Of course, China is an independent political actor and has its own political principles. For example, it recognised HAMAs when it won the 2006 elections in Gaza, a recognition not given by the USA or Israel. And in 2015, it demanded that Israel not use Chinese migrant labour on building settlements in occupied Palestine. And in 2017, the then Chinese Foreign minister, Wang Yi, called the lack of "an independent [Palestinian] state" a "terrible injustice" in a meeting with the then Palestinian foreign minister, Riyad al-Maliki.
On the whole, I would say that China's continued insistence on the rights of the Palestinian's is proving to be a thorn in Israel's side.
Sources: Wikipedia, Foreign Ministry of The PRC and others.