If you used grapes, there might be naturally occurring yeast on the skins, which may start fermentation on its own. That is also a possibility with any actual fruit (as opposed to canned, or treated), but to a lesser extent.
If you used canned or otherwise "ready to go" fruit, it likely has no natural yeasts in there. If you're going to wait for the specific yeast to arrive, put your primary, sealed, in the refrigerator. It will help prevent mold, bacteria, and other nasties from growing while you're waiting. Then, before adding your yeast, be sure to let the batch warm up to room temperature before adding the yeast.
Also, you can use literally any yeast to start fermentation. Each yeast behaves differently, and can add different tastes, ferment faster/slower, etc. but yeast is yeast. It will eat sugar and make alcohol. If you are really worried about a late start, you can even use bread yeast.