PE Analyst - hate my firm, should I look to lateral after only 6 months?

Hey everyone, long-time lurker/poster but recently made a new account.

My dilemma is as follows: got an offer to be an analyst for an infrastructure investment firm, the day I went to sign the contract they said they'd need me to help the advisory team too (they do advisory, direct investments, and asset management), and I said okay. Although I was unhappy about I tried to look on the bright side since I'd be getting a more varied transaction experience.

Now my involvement on the deal team is deplorable, I honestly feel cheated, I came to invest in infrastructure and rejected other offers for this. Moreover I really don't gel with the other people at the firm, I have a few friends of course but overall my 'culture' is very much the opposite of what I've experienced here (missing deadlines and not caring, unorganized managers, way too casual dresscode etc.). On top of that I'm now helping the asset management team as well so it's only getting worse.

Anyways I have quite a few issues with the firm and have decided to leave, the question is when, I've only been working for about 6 months so I wanted to know if that was too early to start looking to lateral. Should I suck it up and wait another 6 months? I'd rather leave ASAP because I feel like I'm wasting my time.

I'm evaluating whether or not to apply to internship positions since I don't have a masters and with only 6 months experience I don't think it would be that weird, am I wrong?

To be clear I'm looking to lateral only to infra PE since it's what I'm passionate about.

For context: I'm in continental Europe, working in my fourth language (but I'm nearly fluent), from a target with relatively bad grades.

Looking forward to your advice.