My first started sleeping through at 2m, stopped at 3m, started again at about 10m, stopped at about 11m, and since then we've had a few phases of it, interspersed with more wake ups. It's mostly settled now she's nearly 4, but still is up at least 4 nights a week albiet usually briefly.
My nearly 2yo, started sleeping through 2 weeks ago. I'll enjoy it while it lasts, as the next regression or teething is likely to throw her off again. Her worst period was 9-12m ish when she was either waking literally 10+ times a night, or for a 3h segment in the middle of the night. And then I was getting up to work.
The upshot being, yes I think 6m is too early to be expecting them to sleep through, and most of my friends children have been nowhere near this (a year plus at least minimum). So, given this may be a bit long haul, you need to make sure they you and your partner out in place measures to maximize your rest. If your baby is bottle or mix fed, he can alternate nights, or take part of the nights, to ensure you get some rest. He can get up in the morning and leave you sleeping as long as possible etc.
Hopefully baby will start sleeping better and these measures won't then be needed, but don't wait thinking that it's likely to be resolved soon, and staying exhausted in the meantime.