I've been a doula for many teens/women who have chosen an adoption plan for their baby.
Language is important. "Give up their baby" can be a hot phrase, the more "PC" term would be chose an adoption plan/chosen an adoption plan or adoptive family.
Some women are very settled in their choice, others not so much. Emotional dystocia can be an issue for those who are not confident with their choice or those who are being coerced. "holding onto" the baby isn't uncommon.
Encourage her to see/hold/take pictures of her baby, even if she doesn't want them now, hold them for her, someday they may be her lifeline. Give her the opportunity/permission for some alone time with her baby.
Give her the choice of having one or both of the adoptive parents there for the birth, or not. It's her choice, she needs to do what she feels is best for her, not anyone else.
Try not to use platitudes like "you're so strong/brave" as often they don't feel strong or brave and being told that over and over can cause some to feel guilt over the emotions that they do feel. (Platitudes about her choice of adoptoin, which is different than telling her how strong she is in labor!)
Be prepared that she might change her mind, it's always a possibility and if she does she may look to you for local resources that will help her parent her baby. Likewise, she wouldn't be deciding to "keep her baby" but instead she will have "chosen to parent."
Hope this helps.