With my first, I kept my social life for the first approx 6 months, as the baby just slept on me in a sling wherever we were. I went to parties, dinners, even a festival, and baby just slept through them. Towards the end of this, the parties became unviable but evenings round friends houses continued - I'd put baby down following the usual routine, and we'd leave just after the inevitable (for her) 11pm feed, settle her in the car seat, and usually transfer fine when we got back home.
Then as she became more aware of different surroundings etc, it stopped being viable, and our social life ground to a halt.
Then we had another child, and then lockdown etc. Now the nearly 4 year old is pretty independent, though still wakes up most nights.
From a social life perspective, it really depends on your parenting styles and things like whether you breastfeed (and are therefore more tied to baby). With my bottle fed baby, I had a night away with friends 3 months in. I've not yet been able to even have an evening away from my bf baby in nearly 2 years (though half of that is with Covid...).
I suspect that feeling back to normal again happens when you are finally getting enough rest, which can be anywhere from 6w to 6y I guess.