Not initially for me no. I was induced, long labour ending up with c section.
The initial moments when my son was born are a blur but after I was stitched up and on my way to recovery I remember the baby was placed in my arms. I was shaking like a leaf (from shock of the delivery or the medication I don't know) but I remember thinking 'I can't hold a baby, I'm a fucking wreck, somebody help'.
Once I was in recovery I was given very sugary tea which claimed my mental flapping arms and I managed to feed the baby.
The next few days in hospital were horrendous. Despite having had a long labour and c section I was expected to be like every other new mother. Including being barked at to get up and have a shower at 9am (when my baby had only been born 7 hours earlier). I was still numb from the epidural at the time and had a cathertar in. If it had been explained to me that I could attempt to stand and take the catheter bag with me, that would've helped. Being shouted at didn't.
That night in hospital I struggled with breastfeeding, no help was given. A midwife eventually came and asked me if was going to tend to my child. This was while I had my boobs out desperately trying to get baby to latch. Shortly after I also had a big bleed which dripped onto the floor. I asked a midwife to help and take the baby while I sorted myself out. She couldn't tend to me straight away. After an hour or so an auxiliary nurse came and mopped the floor around me. I asked if she could help while I went to the toilet, she couldn't, she wasn't allowed. The pity in her eyes was clear.
Eventually a midwife came to me and barked that she would take baby from me for a few hours to give me a sleep. I replied that I didn't want a break, I just wanted to be able to feed my baby. Exasperated by this point I just asked for a bottle of formula. This was given no problem. I was told that a breastfeeding counsellor would see me in the morning. That never happen.
Anyway, after my long rant I just wanted to say that for me it didn't happen initially. I had two stages of waves of love for my baby.
The first came on the second night home. It was the 2012 Olympic opening ceremony. My DH had cooked a lovely dinner and I had a glass of white wine. Baby was in a Moses basket sleeping soundly next to me. I had never felt such a rush of love in that moment and know now that that'll be my moment in time (until I have grandkids :-) )
I also had another intimate 'oh my gosh I love you' moment with my baby at a few months old while he was sleeping on my chest one afternoon, nothing spectacular but I could feel the love tangible flowing from and to him. He also used to pat my back in a reassuring way even when he was a few days old. I know it's just reflex, but was sooo lovely.