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Amazon [amazon.com] has the Raleigh RX24 cyclocross bike for $ 304+tax. Regular/Full price is $ 649. Free prime shipping or slow boat shipping if you don’t have it. Hard to find a real kids CX bike this cheap unless you are looking at used.
Good review here [cxmagazine.com]. Seems like the biggest problem is the odd sized rims which limit future tire choices.