Unlike many A-listers, the Training Day star doesn't have hired help with her newborn. She explained: "I'm doing it without a nanny for now but I'm open to the idea of having a nanny in the future.
"For me that part of being a mother at this early stage is the struggle of not being able to sleep and not knowing what I'm doing and really going through it with her and battling out those nights."
But the actress has found some support from the elder women in her family as well as online parenting forums. Eva said: "[I] read the comment section from other mothers because I find so much solace in that.
"Just knowing that I'm not alone out there and that other moms have gone through the same thing can at least get me through the night."
The Hitch star, who has been dating Ryan, 34, for several years, also revealed the meaning behind their baby girl's beautiful name.
"Ryan and I both love the Esmeralda character from the Victor Hugo novel, The Hunchback Of Notre Dame, and we just think it's a beautiful name." she explained.
"Amada was my grandmother's name. It means 'beloved' in Spanish."
Eva, who was rarely seen in public during her pregnancy, said it was a conscious decision to stay out of the spotlight.
"Ryan and I decided early on to give her as much privacy as we could. And my pregnancy was the first opportunity to give her that. It's such an intimate time for the mother, too.
"I find the media's 'bump watch' obsession to be both intrusive and stressful. So I made a decision to eject myself from it completely."
- Daily Mail