How would trans fluid get in the cooling system? (2002 Chevrolet Silverado 2500)

Is the only way for transmission fluid to get in the cooling system is thru
the oil cooler? Radiator only 1 and a half years old.

Yes. The only point in the transmissions oil system that touches the cooling system is the transmission oil cooler IN the radiator tank. But it is easy to pressure test.

Oddly, the symptoms usually go the other way - coolant in the transmission fluid.

Either way it needs to be check ASAP before your transmission is destroyed.

Are you SURE it is trans fluid in the coolant and not engine oil? As from a bad head gasket?