Thank you a lot for the replies and the clarification.
Maybe I was not completely clear myself:
My intention is to stay the night after my arrival in a Hotel near JFK (and go there by shuttle bus), use the early-morning-jet-lag-hours to assemble my bicycle and start from there.
After Avrin's post I was looking at the metro-possibility - considering the distance to the next metro-stations I might as well cycle into Brooklyn. I was also looking at the possibility with Howard Beach station, but that would mean going back into the airport (with an unboxed, assembled and packed bicycle -not sure if the Hotel shuttle bus will take me...).
According to the NYC bicycle map
https://www.nyc.gov/html/dot/downloads/pdf/nyc-bike-map-2022.pdf, there should be at least some bike-lanes in Brooklyn (?).
I will let you know about my solution if I survive Queen's traffic
.
Thanks a lot for your concerns !