However clear or unclear the specifics of his ethnicity may not be at any point, he is always named Khan Noonien Singh, a name with conspicuously South Asian resonance. That's why even non-Trekkie audience members were able to twig to the oddness of his being played by a white guy. So this really strikes me as being a bit of a dodge.
And when Noonien Soong
turned out to be a white American in TNG...?
(IIRC, he's described as Asian in the TNG Officer's Manual
, which pre-dates the decision to have Brent Spiner play most of Data's family)