After all, Emily Blunt is a mother herself, so the struggle experienced by this fictional mother felt real and palpable to her — albeit in a far more heightened way.
To achieve that level of intensity, it probably also helps that Emily Blunt felt a very important connection to her character while filming A Quiet Place.
In fact, elsewhere in her interview with CinemaBlend, Blunt made a point to note that fact that portraying this mother stood out as one of the most deeply-personal performances of her career, as well as the fact that she related to the struggle of these parents in a more natural way than she did with films like Sicario or The Girl on the Train.