If you and the other biological* 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. The first rule is the parent the child lived with the most. If that is the same (you all three lived in the same house all year), then it's the parent with the highest income (AGI).
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.
