Hi Tkeonce. Welome. You say that you are new to this. I agree with Maylar, that there can be a lengthy lag time as the yeast reconstitute, "wake up" repair themselves, bud (reproduce) before they really begin work on transforming the sugars in the must (the fruit juice before you have pitched (or added) the yeast). BUT... you say the apple juice was "pasteurized". OK. Is it possible that sorbate was added to help lengthen its shelf life? Sorbate will in fact prevent your apple juice from fermenting. If you bought a non alcoholic "cider" - apple juice made simply from pressed apples - sold in chiller cabinets - and which was not filtered then it is often sorbated before being sold to supermarkets. If you bought this from a farmers market it is unlikely to be sorbated and if the juice was clear apple juice (like Mott's or some other national brand) shelved at room temperature, it is unlikely to be sorbated... But the nutritional label will tell you whether the juice you bought can be easily fermented or not. You do not want to see the word "sorbate".
OK, by noticeable reactions, I assume you mean froth or bubbles in an airlock. Cider does not always froth very much- and the seal on your airlock may be defective. The only sure method of determining fermentation is to measure the density (specific gravity) of your must. And you measure this with a glass instrument called a hydrometer (costs about $7.00). Before you pitch the yeast I would expect apple juice to have a specific gravity of about 1.040- 1.050. As the yeast converts the sugar in the fruit to alcohol and carbon dioxide the density drops. It can drop as low as about 0.994 and that means that all the sugar has been converted.
Brewers are near paranoid about taking samples of their brews to measure the density (the specific gravity) and they shudder at the idea of returning the sample to the fermenting carboy. But if you sanitize your measuring cylinder, your hydrometer, the "thief" (could be a baster) that you use to suck up the sample from your carboy and pour into the cylinder you don't need to be fearful that returning the sample will contaminate your cider. I have been fermenting for years and have never contaminated /infected my wines by returning the sample back to an actively fermenting bucket or carboy.