According to GTA Wiki, there are 4 ways to get the Rhino:
Available inside Area 69, but when the base is entered 5 stars wanted level is automatically gained, so don't try to get it until after obtaining the Verdant Meadows safehouse; make a run for it once you get the tank and save to eliminate the stars before parking the Rhino in the hangar.
Will spawn underneath the bridge going above Ganton after 100% is achieved.
Can be spawned by typing the code "aiwprton" during gameplay.
Police will use the tank to stop you once you achieved 6 stars. Save when it comes to clear wanted, try to steal and kill the person inside.
That means that the only way to get it early in the game (and without cheat codes) is by achieving 6 stars, but with the weak disposable weapons you have it will be very hard to get 6 stars and survive long enough to hijack the Rhino.