I think what you are feeling is understandable. Rightly or wrongly, we often have a picture of what birth will be like, especially since some aspects of birth seem so set and unshakeable. That moment when a baby gets lifted out of you and lies on your abdomen and chest all gunky and blood-covered. If you want an olympic analogy, it's crossing the finishing line.
I've never 'crossed the finishing line'. My twins were born by EMCS under GA so the first view I got of them was a few hours after surgery when two tiny, swaddled bundles were shown to me as I retched in agony from the morphine. Honestly, they could have been anyone's babies. It was a rough, rubbish day and so far from the 'best day of my life' ideal I had been hoping for. I'd set a lot of store, foolishly it turned out, in seeing my babies being born. I'd spent five weeks in hospital on bedrest with bleeding and complications and seeing my magic IVF babies being lifted out of me and finding out their sex was going to be my 'reward'. It didn't feel like too much of an expectation, although people will probably trip over themselves to tell me how I should have had NO expectations at all; that expectations just mean disappointment. Well, not for most people. In Real Life I'm the only person I know who has not seen their babies being born. Even now it feels like something people take for granted. No one expects to miss that moment. Plus, it's a very important moment. If you speak to mothers about the first time they saw their baby it's very emotive and intense.
Second time around was going to be different. I was going to try for a VBAC and had all these worse case scenarios lined up in case things went awry and I had another EMCS under GA (my husband was going to get to hold the baby first, someone in theatre was going to take photos of the baby coming out....). Even then, I didn't get it this time either. My baby was born very poorly due to sepsis and inhaled meconium and was born not breathing. He was worked on frantically by a crash team for 8 minutes and then rushed off to NICU. It was pandemonium in the theatre and the moment of the baby being lifted over the cloth, and finding out the sex and holding that baby (that was going to be the balm for the first time that went so awry) was not to be. I got a glimpse of an incubator being whizzed past me whilst I tried not to vomit.
For me, this time, it's okay. I set up so many 'what ifs/worse case scenarios' that I was actually prepared. And I also know, from first time around, that not seeing your babies being born makes no difference with how you bond with them long term. I had awful PND after the birth of my twins and not seeing them being born didn't help with that, but it was only a tiny part of the picture. And once I was through and over that PND I realised the love I had for my daughters was manifest and beyond the universe; there really is no end to it. Perhaps it is even more acute because of the difficulties I went through? Perhaps it burns brighter and sharper because I was so lost in the beginning?
It doesn't mean it doesn't affect you - it can hurt you acutely, can feel a piercing loss. Even now, when I think about it, it makes me sad; in a very happy life it's a true and real sadness. However, it's only a micro part of my life as a mother. As time passes it does become a mere heartbeat in terms of experiences and the sharpness of the disappointment and grief do fade. You just need to allow yourself to feel sad about it. I found writing down a detailed birth story and showing it to a friend really helped as it gave me an understanding of that day and my feelings about it. I allowed myself to feel disappointed, robbed, upset. All those feelings that people would rather we didn't feel as mothers.
I'll never have the moment of my children's birth. That will always be a sadness to me, however much people will say "get over it" or it doesn't matter. But I can promise you in the great scheme of your being a mother, it will only be an atom of sadness. And perhaps we love our babies a little bit sharper for that small piercing loss. I know I do.