Once you finish boot why don't you go airborne. It will be easier right after boot than later on.
Now some serious advice, take it or leave it as you wish.
Don't bust a gut trying to max the first PT test. They are expecting you to progress as you go along. DO start running right now. Be able to run for at least 3 miles now, it will pay off at boot. Do build up your push ups and sit ups. Listen a lot, talk very little no matter how much you think you know now, what you know is either going to be wrong or out of date. Things that do not seem to make much sense at first should turn out to be rather sensible later on when you build more knowledge. There is an old axiom, sweating more in training means less bleeding in combat.
Do not try to be the top soldier and do not try to be the least soldier do learn to BE a soldier. Best of luck. You are joining a long and distinguished line of soldiers in service to the country.