The simple answer to this question is no, mother's do not get preference in custody of children. Though, it may feel that way in the beginning, especially for unmarried fathers. Initially, unmarried father's have no rights to custody of their children (see our others post here about father' rights). In order to establish their rights, they must file a Paternity Action in the correct Court. This is not true for married Fathers, who have completely equal rights to the Mother from the beginning. Though not initially on equal footing, once a father's rights are established, through a paternity action or through a marriage, then parents are presumed equal in terms of their ability to parent. This is true even for all children, even young babies. While Courts must consider what is in the best interest of the child and are not necessarily automatically going to award 50/50 timesharing. They have to evaluate what is in the child's best interest. Having siad that, the reality is, that MOST cases do result in parents have between 40-60% of the overnights with their children.
There are multiple factors that get taken into consideration in determining what is going to be in a child's best interest. In most cases, spending a substantial amount of time with each parent is viewed as best for the children. Certain circumstances make equal time impossible, such as the distance between the parents' homes or a parent's work schedule. When n either parent has any manjor obstacle to parenting and when both have the ability to provide daily care, the general rule is that parents will share time nearly equaly with their children.
Here is a video our founding attorney Leisa Wintz, MS, Esq discussing this the roles of parent in timesharing. https://youtu.be/HE3ZHVwwZDQ