[sudosysgen]

AN/TPY-2 has a 120 degree FoV, and CENTCOM operates them all across the ME, not just in Qatar, but also in Saudi Arabia, the UAE, and in Israel. The likelihood that none of those installations had the ALBMs in range is basically zero.

The chain of actions you're describing would have around 10-15 minutes to be executed.

The likelihood that neither THAAD nor any of the Patriot batteries were sufficiently ready to launch is also basically zero.

THAAD has an engagement range of over 100km, so the battery was undoubtedly in range; and it can cue Qatar's own Patriot batteries so they can launch the missiles; I find it hard to believe there were none in Doha.

So, this would not be a split-second decision - there was quite a bit of time given the proposed trajectory. It's very very unlikely the US didn't have the sensors to see the missiles given the intense concentration of long-range ABM radars in the region.

Is it theoretically possible the US legitimately couldn't do anything? Yes. But the odds are overwhelming that the US knew about the strike with minutes to spare before making a decision, and decided not to protect Qatar.