Whoopee! I get to answer a question!
The cooling fan clutch will temporally engage the fan on cold starts. The whooshing sound is air being drawn by the fan. I believe this is perfectly normal and you shouldn’t be alarmed.
Basically the fluid in the fan clutch has settled and has somewhat thickened. Once the engine is started the fluid is evenly distributed and the fan will quickly disengage. (the fan continues to rotate but at a significantly slower speed)
That’s my prognosis.