It is possible to conceive before your first period, but only if you ovulate, obviously. It's very hard to know when that's happening as sometimes your body has several false starts before it gets going for real. If you think you've ovulated and then you get no period and not pregnant, then you know you didn't ovulate. And everyone is different.
Quite often, cycles only resume once mum has a reasonably long break between breastfeeds (say at least one 6hr-ish break), but again, everyone is very different in this regard.
Good luck!