If you are determined to go, then simply go. You'll be burning the bridge of this current job anyway, so there really isn't a way to keep the bridge usable. Although, with no leave, there's no easy way to even get to the interview without lying or at least taking time off without pay.
If you're still considering all the options, have you considered looking down the road for some more long term options? For instance, how long were you originally planning on staying at this current job? Probably not the rest of your life. Might the other company be an even better place to work when you have some experience in a couple of years? This probably is not the last job that company will ever have open, and they're more likely to want to hire someone with some experience and who behaves professionally over someone who would quit a job after only a week.
If you do want to consider working there in the future, without burning bridges at your current job, then let them know you just accepted a job, but otherwise would love to continue talking to them. Tell them that you'd like to keep in touch, that perhaps in a couple of years, when you have some more experience, they might consider you for a future job opening. And ask if there is something that you should plan on learning or studying in the next couple of years, so that when that opportunity comes, you will be an even stronger candidate.
