Normally, you have to claim a child or dependent to qualify for head of household status.
The only exception might happen when you’re a single parent without custody of your child, but you still meet all the qualifications to claim them as a dependent. In other words, you may be able to claim head of household if you’re unmarried, paid for more than half of the costs to house your child (even though you don’t have custody of them), and your child qualifies as a dependent.
But keep in mind that in order for your child to qualify as a dependent, they have to live with you for more than half the year. And if your child does qualify as a dependent, you definitely want to take advantage of tax credits aimed at helping people with dependents save some dough, like the child tax credit and the child and dependent care credit.