Not very knowledgeable on the subject, but once you have signed an offer letter for any organization, you would have to serve it's notice period at least which would account for anything between 1 to 3 months. Moreover, that doesn't leave a good impression on your current employees. I'd suggest you to tell that to the other company who offered you a position and let them decide if they could extend your offer or they might figure something out for you. Best of luck