How soon after birth for suckling - ASAP
There's no reason to wait (unless there's a problem with you or the baby that means you can't)
I had DD3 for skin to skin while they stitched me up post-CS, and latched her on as soon as I got to recovery.
After a straightforward natural birth you could be doing it moments after birth.
IME the baby will be tired the first night (only had CSs though) so often sleeps more than feeds. Then the second day and night they just Ho for it - feed and feed and feed to bring your milk in.
I don't know why you think they will be worried about supplementing with anything else. All things being equal, they don't do that IME.
The thing that I found really tricky second time, and you might even more so given your previous experience, was how giant a nipple is compared to a newborn baby's mouth.
Your most recent experience of feeding a toddler will bear no resemblance to trying to get a newborn latched properly. I felt a bit daft asking for help from the MWs, but I needed it at first.
Oh yeah - your milk coming in can be a total game changer in terms of feeding. A baby that has been doing fine on colostrum can start to struggle to latch onto rock hard engorged breasts that spray milk everywhere.
But you might find (fingers crossed) that the milk coming in is less dramatic than first time. My boobs were pros second time around. They seemed to just know what to do :o
Oh and - don't express unless you have to. The most efficient way to stimulate your breasts to produce milk is to put your baby to the breast. No expressing machine can match that.
Best of luck :)