I'm with the others. Is it possible? Yes. Will it be the best thing for your child? In rare, unique circumstances, yes...but with a private newborn adoption, those types of circumstances are highly unlikely anyway.
I agree that it's time to really examine your motivations for a closed adoption.
My wife and I also thought we wanted a mostly closed adoption when we started the journey. We initially felt fairly firmly planted in the realm of a semi-open adoption (letters, or *maybe* limited contact with a grandparent or something). The more I researched open adoption, and particularly the more I read the writings of adults who were adopted during their childhoods in the era of closed adoptions as the norm...the more my mind and heart opened.
We now have an open adoption (ds, who we have had since his birth and who is now four), and an adoption we had really hoped would be open but is actually closed (dd, who we have had since she was 6 months and who is now three). I get to see how it works out for both my kids, and frankly, the way it has worked out so far has made me an even bigger supporter of open adoption.
I highly, highly, *highly* recommend grief counseling for any parent who is starting the adoption journey after unsucessful attempts at pregnancy (even if adoption had always been in the cards, but as an "after I get pregnant once" kind of thing).
There are some truths that those of us who are adoptive parents have to wrestle with and eventually accept. These include:
1. Even if we adopt them as newborns, our children have lives and relationships and a history from before us, of which we will never be a part.
2. Related to the above, our children have more parents than just us. Yes, those other parents have an entirely different relationship with our children (aka a non-parenting relationship), but we can't change the reality by keeping our children and their first parents from each other. This is something you can either wrestle with and begin facing and coming to peace with now, or have it jump up and bite you in say, 18 years give or take.
3. We have an extraordinary amount of power as an adoptive parent. Truly. It is hard to see that when you are dependent on someone else in order to have a child. But this moment in time is so brief once your child is in arms and you are looking back. Over our children's lifetime, as adoptive parents, we each hold an extraordinary amount of power. The decisions we make and our attitudes will be completely lifechanging for at least two other folks, not just in a single moment in time but forever. Many, many "birthparents" think they want closed adoptions but later realize (sometimes well after the birth) how problematic that is. You *could* take advantage of the emotional place a birthparent is in prior to placement, but you *would* be taking advantage...for, in all likelihood, your own gain only.
4. When we begin to make decisions for our children, it is time to begin to start thinking like a parent. When we plan an adoption, we make decisions for our child. At that moment, the option of putting what feels best for us-- as the adoptive parents-- first, before the needs of our children, goes out the window. Our children won't be babies forever. Our children will grow into a set of needs in which open adoption will in all likelihood be tremendously helpful. You can convince yourself that closed adoption is better for everyone, not just you...especially because during pregnancy many "birthparents" are likely to feel like it will be too. But having seen what people have written here, you'll know better, and your baby deserves better than that kind of parent self-deception. If you originally set out in a closed-adoption scenario, but express some flexibility should the birthparents change their mind about keeping things closed, you open up a world of positive potential not just for your baby and the birthparent, but also for yourself. I, for one, have loved and enjoyed our family relationships with our son's first parents very much.
5. The adoption journey, which is really a lifetime's journey, transforms us. Whatever you think you know to be true now will be different from what you know to be true in a year, in five years, in ten years. This is not the time-- at the outset-- to start cutting out possibilities.
I say all this with love and realizing that this is all stuff that is difficult to hear. Everyone here could have just answered your question. Yes, it is possible. But from your introduction and from the fact that you asked this question, it is clear you are pretty new to the world of adoption, and that this is probably not how you expected to be bringing a baby into your family. So we are each, in our own ways, trying to answer the question that you can't possibly realize yet that you can't answer while standing in your shoes as a newcomer to this world...which is, "is it right to have a closed adoption?"
I hope you find that the helpful gift that it is intended.
By the way, I am not single (though I know a number of parents who took the same route as me and are), and I am not gay, but I am married to another woman (same-sex marriage), and I have two amazing children adopted through foster care. I wish you could meet my children. Parenting them is nothing to dread