If you and the other parent live together, either one of you (but not both) may claim the child. You may decide between you which one will claim the child. Only if you can’t agree, do the IRS tie breaker rules apply, to see who has first choice. It may be worthwhile to prepare trial returns, both ways, to see which way the family comes out best. This tool may be useful: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1.
If your partner has no earned income, it's almost certain that the family will come out better if you claim the child. In addition to the child tax credit and earned income credit, you probably also qualify for Head of Household HoH) Filing status. HoH rules:
https://turbotax.intuit.com/tax-tips/family/guide-to-filing-taxes-as-head-of-household/L4Nx6DYu9
A common error is when unmarried parents live together, If you and the other parent live together, only one of you can claim the child for any tax benefit. The TurboTax interview is confusing (it's designed for divorced parents, who are allowed to split the child). The second parent should not enter the child, at all.
