What would you do if you find another company which is bigger than the one you are going to? Avoiding the problem causes bigger problems later, and running away from those is never a solution. You need to be mature enough to understand that dreams comes at a price. I think you should resign and serve your notice period and communicate the same to your future employer. This will be right ethically and professionally.
Second, if you don't have time to resign and serve the complete duration of the notice, you should talk to your current employer. No one would like to mess up your career, maybe you can find a mutually agreeable solution to the problem.
If they ask for monetary compensation like disagree to pay you 1 month's salary, then I think if you are desperate to join the other company and think that it will be good for your career, 1 month's salary is quite a little price to pay. Afterall, there is no job better than the job you want to be in and love doing it.
Hope, this would be helpful to you.
Good Luck.