having an interview after having started a job

I have an interview with a great potential of receiving an offer and it would be a MUST start working the following day. At the same time I have another interview (second round) the week after the first one which would be my dream job.

I have seen handling multiple interviews / offers but in my case it was explicitly said that I MUST start the week I do the interview.

I have already said that I was fine with that start date. Please any suggestions will really help.