Just to be clear, the DSP birds looked for ICBM launches (for example).
There was talk of refining the detection capability over 30 years ago to detect cruise missiles. A lot of things have changed in 30+ years. Don’t know what current capabilities are. I can only surmise they are easily better (duh).
The launch detection systems definitely see the hot engines. Capabilities other than that are not going to be advertised. If they were boosted with a SRM, they were seen. The same system would also see the heat of impact/warhead detonation. So even without complete flight path, it would be easy to put two and two together.