Feeling trapped in my new role

I’ve recently joined a Tata group company in a non-texg marketing/comms role with over a decade of work ex. After spending a week here, I’ve realized the culture is way more rigid than I expected- there’s mandatory 9 hrs attendance, no punch in after 10, very little flexibility, and no wfh options. Most of the induction focused on attendance and their regressive policies. Bag checks too. It feels like a school tbh. On top of that, my new manager expected immediate deliverables from day one without giving content or time to understand the business. She seems like a sweet talker but her tone and behaviour towards the team is concerning. People are just glued to their systems all the time. I’ve come from an hybrid EU org and can’t see myself here long term. Plus the 1+ hr of commute is draining me already every day. The work environment for a creative professional feels very restrictive (even internet access on phone and sites like Gmail are limited). So I can’t give interviews easily while employed here.

There were signs during the interview process but I decided to not overthink. I know I wont stay long term here for sure. Should I spend a month here just for the salary or start planning my exit immediately? My notice period during probation is a month. Some sane advice would be helpful.