Can I find a sibling fathered by my birth father without knowing the mother's full name?

Good luck. I can’t even find my birth father.

All you know is her first name? You don’t know if she had a boy or girl? Or even the right year?
You are asking quite a bit.

If you are willing to spend the money, I would suggest going to an investigator that specializes in finding birth families. The birth mother may have listed your father on the birth certificate, if she did, that will make it easier.

just do the investigator thing.

good luck. :) god bless you