I got offered to a better job just after I accepted a new job

I'm a graduate level Civil Engineer, this will be my very first time working full time.

2 weeks ago, I was accepted to a small company, far from home (I basically have to move out) in a small city. To be honest, the main reason why I accepted that one was because I was anxious I would not get any job at all, 1 is better than nothing. Then just recently, I got offered to a better job, big company, in my city so I don't have to travel too far.

It is obvious that I really want the job at the bugger company, but would it be unethical to turn down the job that I just recently accepted? What do you think?

P.S: I haven't started working at the small company yet, I'm still currently a student and waiting for my graduation which is only months away.

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