Hello girls. Just after a little advice and a bit of reassurance that we're doing OK.

My little girl was born last Tuesday almost 4 weeks early. She was born via urgent c-section after her growth rate slowed dramatically.

As she was so early, it has taken a while for her to gain the suck reflex properly and in the hospital I was hand expressing my colostrum and she was being syringe fed. She would occasionally go to the breast and I was offering it every feed, she would latch, suck for a bit and then let go.
On the third night, after hours of trying to get her to feed, her screaming, me crying, threats of a nasal gastric tube and the room in disarray I finally relented and allowed her to be topped up with formula. So- the rest of the time in hospital I pumped, offered the breast and topped up with formula.
I am home now, it is day 6 (she was born at 3pm so not true day 7 until this afternoon) and my milk still isn't in fully.
I am still expressing, using hand and the pump, every two to three hours and every feed she gets offered the breast, she will still latch and usually will suckle on and off for 5-10 mins. She latches really well, does a few big sucks and then kinda falls off and needs to be put back on. After 10 mins of breast or if she starts getting upset she gets given anything I had expressed after her last feed. At the moment, after working on it for a while, I'm getting about 50 mls which seems to be keeping her happy. If she is still hungry, she will take 10-20 mls of formula.

I am hoping that when my milk comes in (hence the still waiting......) feeding will be easier for her and she will suckle for longer and not need the bottle any more.
Can I have some reassurance please that it's still early days and there is still time for the milk to come!! I am exhausted after feeding her and then having to pump for 30 mins as well. Please don't comment if you are going to give me "formula is bad" comments. I feed guilty as it is that we've had her on it but if it was that or losing her to the SCN and a gastric tube- it's a no brainer to me!

Also- any advice people have to encourage my milk to come in. We are doing lots of skin to skin, regular pumping and getting her to suckle when I can. Any other tips?