leads suddenly becomes parents

Not quite but close...

• Warm Time With You (FL is raising her nephew and the ML who is the child's uncle but the FL has never met moves in, initially to get custody)
• Please Be Married (the child is actually their's from the future but neither knows/believes it. The leads meet and end up moving in together, co-parenting the child.)
• Please Be My Family (leads are each a single parent to their niece and nephew, then get married and raise the kids together)
• Legally, Dad (FL is struggling to raise her younger sister after their parents die and makes a deal with the ML)
• Renai Mangaka (ML looks after his nephew after his brother suddenly dies, the FL meets him at the funeral and starts living with the two)

https://mydramalist.com/discussions/korean-dramas-movies-variety-shows/61579-looking-for-drama-where-suddenly-taking-care-of-a-kid