For awareness, although a child record is most often created as part of the associated baby blessing, the blessing is not required. GHB 38.2.6.1 refers specifically to ordinances, and a child blessing does not apply as it is not an ordinance, and does not appear in any membership records. GHB 18.6.3 talks about the Child Record Form and Blessing Certificate, and refers to the LCR page for creating a Child Record. The blank form you can print from that page indicates that the baby blessing is optional, and if it was performed, a blessing certificate can be printed after the child record is created.
So if no member record exists for the baby, I would go ahead and create that record in your own ward. You can do that without needing any information about the date of a baby blessing, or information about who performed the blessing.