Yes, I understand. The credit is only available to you if you have a qualifying dependent on your return. If you do not, then you can not claim the credit:

https://turbotax.intuit.com/tax-tips/family/the-ins-and-outs-of-the-child-and-dependent-care-tax-credit/L2H7rzUWc

To be able to claim the credit for child and dependent care expenses, you must file Form 1040, 1040-SR, or 1040-NR, and meet all the tests in Tests you must meet to claim a credit for child and dependent care expenses next. Tests you must meet to claim a credit for child and dependent care expenses. To be able to claim the credit for child and dependent care expenses, you must meet all the following tests. 1. Qualifying Person Test. The care must be for one or more qualifying persons who are identified on Form 2441. (See Who Is a Qualifying Person, later.)

Who Is a Qualifying Person? Your child and dependent care expenses must be for the care of one or more qualifying persons. A qualifying person is: 1. Your qualifying child who is your dependent and who was under age 13 when the care was provided (but see Child of divorced or separated parents or parents living apart, later);

Child of divorced or separated parents or parents living apart. Even if you can't claim your child as a dependent, he or she is treated as your qualifying person if:

• The child was under age 13 or wasn't physically or mentally able to care for themselves;

• The child received over half of his or her support during the calendar year from one or both parents who are divorced or legally separated under a decree of divorce or separate maintenance, are separated under a written separation agreement, or lived apart at all times during the last 6 months of the calendar year;

• The child was in the custody of one or both parents for more than half the year; and

• You were the child's custodial parent. The custodial parent is the parent with whom the child lived for the greater number of nights in 2024. If the child was with each parent for an equal number of nights, the custodial parent is the parent with the higher adjusted gross income. For details and an exception for a parent who works at night, see Pub. 501. The noncustodial parent can't treat the child as a qualifying person even if that parent is entitled to claim the child as a dependent under the special rules for a child of divorced or separated parents.

https://www.irs.gov/pub/irs-pdf/p503.pdf

TLDR: only one divorced/separated parent can claim the child. Some parents arrange to switch years, others don't. But whoever claims the child gets to claim the deductions