WWYD: Stay with high paying offer or drop for TFA?

Hey guys,

So I went through corporate recruiting at a top target school and got a rotational management offer from a relatively anonymous multibillion dollar eCommerce company. During the interview process it seemed like it would be a mix of strategy, process improvement, and talent management which seemed great so I accepted and dropped out of all my other final round interviews and offers MBB consulting and more well known LDPs). It's only been a month since I've had the offer and I'm really really really starting to regret it. The pay and benefits are great (100k+ total comp) and people do manage to go to M7 business schools but after talking to a couple of alumni from my school the job seems a lot more general management/talent management with the occasional process improvement project and 0 strategy. I was really really hoping to do strategy or business analysis work when I graduated.

However a lot of the opportunities have passed now and I don't actually have anything else secured. I was really heavily considering TFA before I accepted the eCommerce offer and I am pretty passionate about education. I talked to the recruiter alot and I feel like it would be more aligned with my interests and save me from feeling suffocated. I think the main issue with the current job I accepted is I'm really not excited about the work I would be doing and it lacks flexibility.

So a few of my questions
1.Would you go with TFA instead?
2.Do you think having a more operations oriented background at the start of your career prevents you from transitioning into strategy or business analysis later in your career?
3. How badly do you think the signaling issue might affect my next career move(literally no one has ever heard of this random company but it somehow recruit at ivies)
4. Would you choose a lower paying small strategy boutique (not name brand) instead of this eCommerce management job?

Any feedback is greatly appreciated! I've been mulling over this for weeks.