Background:
I was job hunting for the past 5 weeks. I applied for Company A (dream company) and Company B at the same time. Company A's recruitment process is comprised of 5 steps, while Company B's recruitment process is only short.
As expected, I finished Company B's recruitment process earlier than Company A by 1 week. They eventually offered me the job. At that point, I just finished step 5 of my dream job's (Company A) recruitment process. I asked Company B to give me an extension to decide if I should accept the offer or not. They, however, declined.
I was not sure if I did well in step 5 of Company A's recruitment process, and I need money to pay my bills for the upcoming months. These led me to accept Company B's offer. A week later, Company A told me that I passed all 5 steps of the recruitment process. Their offer was in many ways better than Company B's, but there's a catch: my commencement date at Company A is on October (2 months from now).
I badly want that job and I know that by accepting it I can grow better in my career, especially since the company's name alone can open many doors. However, I am not exactly sure how to handle this as I have to choose between my personal interests and the company's welfare. I want the best of both.
Question
I have just started last week at Company B, and I still have 2 months left to exit gracefully. The contract allows me to leave early with a week's notice. I want to tell my employer that I'm gonna be leaving by the end of September so that they can prepare earlier for my exit. Would that be advisable? Is it better to just give them my notice exactly 1 week before leaving?