Well China's known to have completed many ballistic missile intercepts since I can remember. I recall several being reported even before 2010. Let's also remember that China conducted an ASAT which is technically more difficult than BMD. Done with a kinetic kill warhead on the first shot back in 2007. During the last decade an a half, we've heard about Chinese BMD including hints that some or all could be designated as HQ-19, HQ-26, HQ-29, and SC-x series.
China's first attempts at starting BMD programs began back in the 1960s with the FJ program and Project 640. These came out with at least the HQ-1, HQ-4, and HQ-81 missiles. None of this BMD business is new for China. In fact the radar side of the problem has long been even stronger. Radar isn't half an issue. EW, Countermeasure and defeating countermeasures are probably greater struggles on the digital side.
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HQ-4 BMD
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FJ-1 aka HQ-81 missile
None of China's previous BMD programs really had much worth just like the American and Soviet counterparts. They were utterly pointless because the limits in fuel and guidance tech simply didn't guarantee much if anything and then there is the geographic positioning and range issue. After all that there is the numbers/attrition problem. The numbers problem still exist but if you're aim is to defeat North Korean or Indian missiles from hitting important targets, then these are absolutely must haves.
What makes SM-3 arguably the most effective ABM system is its mobility or rather the mobility of the platform it sits on. China has no such equivalent.