How much more time should I give the company until it's acceptable to leave?

The considerations here are:
- Your current employer
- Future employer interviewers
- Yourself

As for your current employer, you should give the standard 2-3 weeks notice. But
it would be unwise to do so until you have something lined up.

Your future interviewers are going to ask you why you left this job so soon after
joining. It will be a cause for intense curiosity and questions.

If you hate your job so much, you can't exactly deny its effects on you. Note,
though, that you are surely learning a lot (and a lot of what you're learning is
not apparent to you right now - you'll see later what you got out of this ex-
perience).

So what the [deleted] do you do again? You're talking in all these vague terms ("passion", "creativity") but yet you give no examples of anything you mention. What do you do? Why it isnt creative? How do you think it could be creative? Etc.
If you'd tell us we could say "Oh right yeah that kind of work is like that, change positions" or something you know...

If you are in a bad situation job wise and its not you but the fit is just so off that stay will do more harm to you personally than going, my advice is leave. I have been in that situation and stuck around worst option ever, my last year at the job was hell to be honest (bad fit, reason I was on the project was kicked off the project all kinds of things that just killed my motivation to go to work), the only option in that case is leave.

Verbally accepting an offer is not the same as actually signing the contract you can back out of these things, its not great to do this but you haven't signed anything yet so there is no real legal obligation yet.

Also never ever accept an offer if anything feels off, even if its the littlest thing you (the reason why my last job was such a bad fit).

The hardest thing to learn when entering the games industry I found is that it's a job at the end of the day. What this means is that you have to make sure for yourself that the job you accept fits with you, you are more important than the company when it gets down to the line for yourself.

In the first year on my first game(DiRT2) I learnt more about writing software and implementing things than I ever did on my own to be honest so keep that in mind too, as mentioned in previous messages

Verbally accepting an offer is not the same as actually signing the contract you can back out of these things, its not great to do this but you haven't signed anything yet so there is no real legal obligation yet.

Good point. I did that once, actually. I had verbally accepted an offer, but then
got a better offer from Activision. I went back and turned down the offer I'd
accepted earlier - the hirer wasn't happy, but I was! Taking that Activision job
turned into 12 great years.

I was in the same situation when I moved into game development. It was AAA mobile and I was a gameplay programmer back then, the tasks were ridiculously mundane where most people in my team spent 90% of the time implementing UI.

Oh, and the game was already released when I joined and was on game evolution the entire time, basically very little got updated other than adding new characters and UI.

This lasted until a big update was due to release and they needed a graphics programmer for some new features. Luckily no one else had any real graphics experience and I managed to pick that up, and I have continued on that path ever since.

So I guess you just have to find the window of opportunity and take it at the right moment. Talk to more people, and see what else you can do.