My baby was born at 34+1, but by vaginal delivery rather than c-section (not sure if this makes a difference). Skin to skin was also virtually non-existent as he was taken to NICU, like yours.
I was given a leaflet on hand expressing and a couple of syringes, but no other information and no conversation about breastfeeding, and I didn't realise at the time the importance of skin to skin or initiating breastfeeding/pumping early to encourage milk supply. I tried hand expressing but got nothing, and I didn't start pumping until more then 24 hours after he was born, when one of the NICU nurses talked to me about breastfeeding and I was given a hospital pump to use. I was devastated because I thought I'd missed my chance to breastfeed.
Pumping was hard and I got tiny amounts of colostrum and later runny amounts of milk. I never really got on with the pump to be honest, and my little one struggled to latch as he was so early. He was tube fed for around 10 days - a mixture of formula and breast milk/colostrum (though a higher percentage of formula as I didn't have much milk). He eventually did get the hang of latching using nipple shields to help him, and he was discharged after 2 weeks exclusively breastfeeding.
His weight gain was slow to begin with and we were under the infant feeding team for a long time, but we did manage to EBF for 4 months, then mixed feed (introduced formula on the advice of the hospital to encourage weight gain, although the infant feeding team had been telling me that there was no need to). I wish I'd gone to mixed feeding sooner really as my milk supply was never copious and I honestly think he thrived better on mixed feeding than EBF (he gained a lot of weight quite quickly, seemed to get stronger and then found breastfeeding easier. He also had prolonged jaundice until 4 months, which resolved almost immediately when I introduced formula, unsure if this was just coincidence or not).
He's just turned 3 now, and he's still breastfeeding (though I'm trying to gently encourage him to stop because, to be honest, I've been ready to stop for a long time now and I want my bloody boobs back).
Sorry for the long essay, but what I'm trying to say is that it is likely still possible for you to breastfeed, even if you've had a really slow start. It was possible for me. I felt terrible in NICU seeing all the posters about "golden hour" (which we never got) and seeing other mums producing what I perceived to be loads of milk, when I was only getting 10-15ml from each breast even after over a week. But we did eventually manage to breastfeed and I have a happy and healthy 3 year old now.
I do wish that I hadn't put so much pressure on myself though, and I wish I'd switched to mixed feeding sooner (but I felt under a lot of pressure, even from the feeding team, to persevere with EBF). If breastfeeding doesn't work out for you then so be it - you can still have amazing cuddles and an amazing bond with your baby without it. I know it's easier said than done, but try not to drive yourself mad over it, in a year it won't seem important, and your baby will be fine either way.