Congratulations on your beautiful baby girl!
My DC1 was poorly at birth and needed 10 days IV antibiotics, so we had to stay in hospital. Feeding was tricky (in hindsight, simply because he was too exhausted (from being ill) to be able to feed, so got even more exhausted due to not getting enough milk...) to the extent that after 5 days he had to be tube fed.
We did eventually establish breastfeeding, and in the end he BFed until nearly 2yo. But though it has been a long time, I remember well how worried and sad I felt at the time, I shed many a tear. So your post resonated and I didn't want to leave it unanswered!
It took a lot of effort and came with ups and downs...
I started pumping in the hospital when he was on the tube, and it was highly frustrating because the milk was measured and I was constantly sailing at the limit - always needing to get another x ml out or he would have to be topped up with formula. I was basically feeding all day long every day (if you include trying to BF, then pumping, then sterilising - the whole process took about 90 minutes, and had to be repeated every three hours, so 90 minutes feeding, 90 minutes break).
I was lucky that the pumping did work and my milk started to flow and I'd get a lot out, enough to have spare. And with milk flowing like that I got DS back onto the breast when they finally removed the tube.
But only 10 days after we had left hospital, we were back again - because DS was losing weight again, and sleeping too much, he had basically fallen back into that negative cycle of being too tired to feed-not getting enough energy-being even more tired.
The doctor at A&E where we ended up, said drily, "Well of course he is screaming, he is hungry - starving in fact! Just give him a bottle already!" Which was rather painful to hear...
This time we did start giving him bottles. I had some frozen milk left over from before, and by the time that was gone, I had the pumping back up and so for the next 4 weeks or so he had EBM by bottle. Again, this was very hard work.
In this time we saw a BF counsellor who was brilliant, very reassuring, and basically provided us with a plan to get him back onto the breast. It's been nearly a decade so I am hazy on the details, but the plan involved gradually reducing bottle feeds and swapping them for BF.
By the time he was 10 weeks old, he was fully back on the breast.
(And though he had been 100% bottle fed at one point, he never ever took a bottle again after that - which was a bit of a headache when he started going to a childminder later on...)
So it can work out. If you really want to BF, do persevere with the pumping, it often takes a little while to get going properly. Make sure you make a good attempt at the breast each 'mealtime' before pumping, and make sure you get yourself a good pump.
However please remember also that the right way to feed a baby is the way that works for you and gets baby fed. I don't personally regret all the effort I put in at the time, but I would always hesitate to recommend it to anyone else, as it took so much out of me and DP, we were both totally shattered and unable to fully 'enjoy our baby'.
DC2 was 100% bottle and formula fed, and this is also a beautiful bonding experience. Some perks, some disadvantages compared to BF (the established, well working kind of BF), but at least we never had that extremely tiring phase of BF-not-working-well.
Good luck in finding a way that works for you!