Meet with the judge at your scheduled date and explain your reason for wanting the adoption records unsealed. Generally, you will have a better chance if your reasoning isn't based solely on personal desire or interest. Medical issues are the most common reason sealed adoption records are unsealed. However, you can consult an adoption lawyer to build the best argument no matter what your reasoning. The judge will either grant your petition and unseal the records or deny your petition. If this happens, you can request a confidential intermediary.
When the birth mother has narrowed down her prospective adoptive parents to one or a few families, normally they arrange to meet in person. Good adoption agencies and attorneys do this in a pressure-free setting where no one is encouraged to make an immediate decision. If they are geographically distant from each other (as some adoptions are interstate, with the birth mother living in a different state from the adoptive parents), the first meeting will normally be by phone, then advance to a face-to-face meeting if the meeting by phone went as well as hoped.