When do you actually feel like a "real parent"?

So my son is 4 months old now and I STILL feel like I'm playing house sometimes. Like I'm babysitting and his real parent will come pick him up soon. Is that normal? I change diapers, do feeds, handle bedtime, all of it, but there's this weird imposter feeling. My wife said she felt the same way around 6 months so maybe it's just a timeline thing? But it's kind of unsettling to be honest.