Have you considered that the problem could derive from hunger, not sleep?
I mention this because in the first 3 ish months (the newborn phase) sleep should be relatively passive and easy, compared to post 4 months. In this newborn stage as long as all needs are met then baby should sleep. The most simple and obvious reason for baby not sleeping would be lack of calories.
Not feeding to sleep is very telling. It's ususlly pretty difficult not to feed to sleep as a newborn. Light sleeping is also worsened by low level hunger.
So my first suggestion would be to focus on feeding.
On from this, make sleep as easy as possible for baby. So if she sleeps while you are holding her - sit yourself down and keep holding her. If she sleeps being rocked in the pushchair - keep perpetually rocking the pushchair and don't stop the movement.
(Incidentally, bouncy chair is great for a baby who likes perpetual movement. Foot bounce baby while you sit on the sofa)
I suspect that the mistake you are making is the assumption that you should be able to just get her to sleep (holding her, rocking her etc) then stop. That time will come, evidently not yet. So you have to keep it going as much as is possible in the daytime.
Cosleeping (at night and for naps) may help. The idea is not moving a sleeping baby. You feed to sleep lying down and keep baby there.
And continue with no more than an hour awake. You may be into an over tiredness cycle. All bets are off once baby is over tired - you need to them then go into a situation of "any sleep, any how". However you can possibly get as much sleep as possible from baby, do that just to get baby sleeping.
I would really concentrate on feeding though. It's a hard conversation to have with anyone EBF, but the "never fails" answer in the newborn weeks should be feeding to a milk coma - at the breast or with a bottle of formula.