Yes, it is possible for you to claim Head of Household even if your divorce decree states your ex claims your child for 2019. Here are the conditions for non-custodial parents to claim HOH:
The IRS states:
Children of divorced or separated parents.
A child will be treated as the qualifying child or qualifying relative of his or her noncustodial parent (defined later) if all of the following conditions apply.
1. The parents are divorced, legally separated, separated under a written separation agreement, or lived apart at all times during the last 6 months of 2019 (whether or not they are or were married).
2. The child received over half of his or her support for 2019 from the parents (and the rules on Multiple support agreements, later, don’t apply). Support of a child received from a parent's spouse is treated as provided by the parent.
3. The child is in custody of one or both of the parents for more than half of 2019.
4. Either of the following applies.
a. The custodial parent signs Form 8332 or a substantially similar statement that he or she won't claim the child as a dependent for 2019, and the noncustodial parent includes a copy of the form or statement with his or her return. If the divorce decree or separation agreement went into effect after 1984 and before 2009, the noncustodial parent may be able to include certain pages from the decree or agreement instead of Form 8332. See Post-1984 and pre-2009 decree or agreement and Post-2008 decree or agreement.
b. A pre-1985 decree of divorce or separate maintenance or written separation agreement between the parents provides that the noncustodial parent can claim the child as a dependent, and the noncustodial parent provides at least $600 for support of the child during 2019.
If conditions (1) through (4) apply, only the noncustodial parent can claim the child for purposes of the child tax credits and credit for other dependents (lines 13a and 18b). However, this doesn't allow the noncustodial parent to claim head of household filing status, the credit for child and dependent care expenses, the exclusion for dependent care benefits, the earned income credit, or the health coverage tax credit. The custodial parent or another taxpayer, if eligible, can claim the child for the earned income credit and these other benefits. See Pub. 501 for details.
From IRS https://www.irs.gov/pub/irs-pdf/i1040gi.pdf
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