Firstly, you realise that high speed and ground hugging are mutually exclusive right? A terrain hugging supersonic cruise missile will either smear itself across the first mountain it comes across or rip its own wings off trying to turn around it at supersonic speeds. Remember rockets cannot throttle like engines, so it’s not like the Brahmos can slow down and speed up as terrain shifts. It’s one speed all the way.
Also, you will not achieve anything close to max range in low level flight c
High speed and ground-hugging aren't mutually exclusive when you consider missiles like the Klub, which sea-skim until they make a supersonic dash at their last stage.
That said, the Brahmos is rocket x ramjet, which implies it'll be trapped around Mach 3-4 once the ramjet takes over, which'll be soon in an air-launch.
Also, the interception scenario you've posited is very legalistic, when as Trump has demonstrated in the United States, law doesn't matter if you control public opinion. Shooting down Indian airplanes over Indian airspace will be diplomatically very damaging to China, and what's more, the InAF forces in the North are in the range of 200-300 planes. This is a huge number for the PLAAF to handle, especially once they're up in the air. The PLAAF has over 800 4th generation planes in inventory, but the number of 4.5th gen planes (i.e, AESA-ed) are likely to be in a similar number as the InAF. A massive air armada will be a challenge to deal with unless the PLAAF is ready to deploy 200-300 planes on their side. More realistically, you need the missile interception capabilities, i.e, PL-10 ASRs have to be deployed within range to shoot down the Brahmos.
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Indian inventories of Brahmos are estimated in the 500s range, I'd estimate based on their numbers that the Brahmos-A with the capability to strike deep into Chinese territory shouldn't exceed 200.
The basic reason aircraft became superior against naval craft in WW2 was because of their speed and ability to concentrate firepower. The same problem applies to China; you should assume you'd need two missiles for interception vs Indian cruise missiles. That means you'd need 200-400 SAMs at any given location to shoot down a Brahmos alpha strike.
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Basically, the PLA is in trouble until November 4th, because as long as the American election is up in the air, China has difficulty making overly aggressive moves. Once the election is over, it either doesn't matter (Trump wins) or doesn't matter (Biden is traditional American risk-averse leadership). Then even if the Indians launch a strong first strike, a counterstrike by the PLAAF could easily take out their offensive assets.