Will quitting a job after a week or month of starting at a company to join my dream company make me look bad to my dream company?

I received an offer from company A and accepted it as I’ve been unemployed for 10 months now. I’ll be starting at company A in beginning of February. I recently interviewed with company B, which is actually my dream company and may or may not get an offer. I’m still in the decision making process with company B. I had to take company A as the decision end date was the day after the interview with company B and I needed company A as my backup basically.

If I do get an offer: If I start working for company A and then quit after a week or month of working for company A and then move to company B will it make me look bad to company B? I’m afraid company B will find out I worked for another company for one week - a month that I didn’t list on my resume before joining them.

I have no problem ending things like this with company A like this as company B is really a top tier company, my resume is set for life type of company. Of course I’m not going to try to burn bridges as I leave.

To make things more complicated, the reason why I didn’t ask my recruiter to expedite the decision is because I wanted to travel before starting company B and thought by asking for an expedition I wouldn’t be able to ask for a later start date.

Should I be transparent with my recruiter at company B and tell him I’ve already accepted the offer from company A and my start date for company A but that I’m willing to move for company B?

Even though it’s not guaranteed that I’ll receive an offer I want to iron out the situation now than get super stressed out later on if I actually do receive an offer.

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