It's a little complicated because your child was born out of wedlock and you are the father. To transmit US citizenship to a child born abroad out of wedlock to a US citizen father, the conditions is that, not only do you have to have been physically present in the US before the child's birth for a total of 5 years, including 2 years after you turned 14, but also, the following conditions must be met before the child is 18:
The child's paternity is acknowledged by you or determined by a competent court, and
You make a written promise under oath to support the child until the child is 18
Usually, when you do a CRBA, the conditions above are satisfied, as they will make you (the US citizen father) sign a document under oath that satisfies those conditions at the same time. But if you try to claim the child's citizenship without getting a CRBA, then you will have to satisfy the conditions in some other way first.
The CRBA would have noramlly been a week or two process -- certainly not worth having created this complication. Also, the consulate would have know that you were a US citizen even though the child had a Jamaican passport, since you have to be a US citizen to file the K-1 petition. They should have asked about it. Are you listed on your son's birth certificate?
