First, if you have concerns about Strategy&'s culture, why did you apply for them?

Second, what do you mean by “bad culture”? It is a poorly defined term.

Third, moving from Strategy& to MBB is definitely possible. 

Forth, in ME Strategy& has a fantastic positioning, better than that of some of the MBB.

I would not join Strategy& just to move into MBB later. There is no guarantee of such a move happening. If you are not happy with Strategy & do not join them in MEA, you will feel stuck and helpless.

Alternatively you can join with an open mind and see what it is like. Every office has nice people and mentors you can work with to learn and grow in your career.

“Is it easy to get into MBB after joining Strategy &?”

First, it is never easy. Is it easier?

Using Strategy& to go to MBB… is not a great stepping stone, to be honest, although that really depends on your starting point. 

If it improves your resume value significantly, it can help. Otherwise, not really. It can be just as hard as going from where you are to MBB.

The exception here is if you are looking to work for MBB in Dubai. In that case, moving to Dubai to work in consulting, can help. Both because you become a “local resource” and because once you're there you can use your time to network with people from MBB (and given the “expat market” characteristics of the location, networking is easier than in other places). 

In contradiction with a lot of answers on this post, if you do join Strategy & and get promoted over a couple of years of experience, you do have a high chance of joining MBB firms later on. The question is, will you want to? Strategy &'s culture might be slightly worse than MBB firms, but they do offer better compensation packages. In addition, a big portion of the current Bain partners in Dubai used to actually work at Strategy & and made the transition when they noticed they can have a bigger impact especially in the public sector given that they had amassed a strong portfolio and network over time. 

I've submitted an application to S&, would you mind if I asked you some questions?

Dubai offices in general have bad cultures (compared to European offices).