I had an ELCS recently - no skin to skin in theatre, but I made sure that as soon as I was in recovery, I just shoved DS down the front of my gown so he was resting on my chest. He seemed sort of half awake (is my 1st DC, so I have no others to compare him to), so I squeezed some colostrum out, rubbed it round my nipple, then squeezed out a little more and gradually 'nudged' him towards my breast.
I just mean I did it in stages, moving him a few inches, letting him lift his head a tiny bit, then moved him again. I wanted him to latch on asap and get colostrum, but I also thought that just shoving my boob in his mouth seemed a bit forceful. I also rubbed a tiny bit of colostrum on his lips to get him licking.
After about ten mins or so, he was on my boob and chomping lightly away. I was in the recovery bed, so mostly lying down - I think I had him lying slightly across me/up mein a loose cradle hold. I made sure I kept him very much with me and on top of me in hospital - he only really went in those fishtank cradles to have his nappy changed, and then came back to me. I think you have to be a bit wary of MWs taking your baby off you when you're post-operative. I think they worry that if you seem sleepy or doped out, the baby is 'safer' in a cot than in bed with you. I'm sure in extreme cases that's true, but while it may be easier in the short term to leave a newborn in a hospital cot, I don't see how it helps establish BF at all.
I also think there's a sort of assumption that the baby will be brought to you for feeds, and then put down in his cradle 'between feeds.' This didn't make sense to me. DS seemed to nap and snack in such short bursts, and I wanted him to feed as much as possible, so it seemed sensible to keep him on my chest as much as possible.
(there was no BF support or advice at the hospital, btw - one MW observed in passing that my nipples 'stuck out' a lot, which was helpful for BF-ing, apparently. That was it.)
DS is now 10 weeks, EBF-ing with no problems and gaining weight very well.