I got a job, then they told me I'd have to start at 6 AM, I said no, then they said 7 AM. Still hesitant?

I got a remote agency job on the east coast of the U.S. and I am on the west coast, three hours behind them.

Throughout the interview process I kept asking about my start time, and they said "depends on the client" but assured me I "would only have to get up early occasionally" to which I replied "oh that's good". I get the job, and they assign me to a client. I ask "what time zone is the client in?". They don't answer but schedule a meeting with the person who would be my manager on the project.

They didn't communicate to her that I was on the west coast, and of course the client they assign me to requires daily meeting at 6 AM my time and they won't accommodate for my time zone. This project last for at least a year if not more. I say I cannot sustain that, but could do a 7:45/8AM start time and honesty 7:45 is pushing it a little for comfort. They come back and say they can assign me to a new project that would require me to start at 7 AM. That's better...but still really early. For context, I'm a UX designer so flexible hours or regular 9-5 hours are generally standard.

What would you do in this scenario? I'm starting to feel guilty for wanting an 8/9AM start time. Times are tough and getting a job is hard, and I also invested around 48 hours of time into the interview process with them so I'm really struggling to make a decision.

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