I took a leave from work after having a new baby mid-2020. Can I take the self employed family leave credit if my leave wasn't directly due to COVID?

[DMarkM1]

No, the reasons listed for the new sick and the family leave credits are all Covid related. The same rules apply to the self-employed.   Here is a link for reference.

The are no other family leave credits available for self-employed taxpayers.

The Family Leave credit is for periods of leave during which they are unable to work or telework due to a need for leave to care for a child of such employee if the child’s school or place of care has been closed (including the closure of a summer camp, summer enrichment program, or other summer program), or because the child care provider of the child is unavailable, for reasons related to COVID-19. 

The sick leave credit is for:

  An employee who is unable to work (including telework) because of coronavirus quarantine or self-quarantine or has coronavirus symptoms and is seeking a medical diagnosis. 

An employee who is unable to work due to caring for someone with coronavirus, or caring for a child because the child’s school or place of care is closed, or the paid child care provider is unavailable due to the coronavirus.