How long is a piece of string? Some babies will start to reliably sleep longer stretches a few weeks in and some won't. There is no one answer people can give you.
The only thing you can do is try to maximise your sleep until your baby's sleep starts to lengthen and regulate, everything they're doing now is completely normal I'm afraid. Sleep in shifts with your partner if you have one, co sleep if you're able to safely, whatever you need to do to make the most of your situation.
You can't change your baby, you can only change your response to the situation.
Also, and you probably won't believe me yet, but you just get used to shit sleep. Once my baby started sleeping through for a few months we had a night of teething related shit sleep that wasn't as bad as our usual bad nights when he was younger, and I felt absolutely dead. But yet used to do it every day for months! Your body and mind just adjust.
This is how my baby's sleep was, to give you an idea of how non-linear it can be:
0-2 months- normal newborn shit
2-4 months- absolutely fucking awful. Only slept on one of us for all day and night sleep.
4-6 months- slightly less shit. Started cat naps in buggy and crib
6-8 months- slept through. Every night.
8-10 months- shit. Awake a lot each night
10-12 months- absolutely fucking awful, would be awake for 4+ hours each night
12-18 months (now)- slept through every night except 2 when he was teething. Naps for 2 hours in his cot or one hour in the car or buggy