In modern Pokemon games, stats are recalculated every time a parameter like EVs is changed; so the EVs gained from Poke Pelago are 'applied' to your Pokemon instantly. In past generations, EVs are recalculated mainly after level-up, so you'd get latent EVs that do nothing until the next level up. You don't have to worry about that in Gen 7, though.
I'm mostly answering this question to give extra clarity on how EVs affect Pokemon at each level, because the existing answer is a little bit misleading. It's true that at level 100, the amount of EVs needed to gain an extra stat point is at its lowest; however, it is no better proportionately than at any other level. The effectiveness of EVs scales down linearly with level, just like base stats and every other parameter. Precisely, the amount of EVs needed to increase a stat by 1 is equal to
floor(400/level) (usually, as you'll see).
The amount of EVs needed for low-level Pokemon to gain another stat point is distorted by the heavy impact of integer rounding at those levels. Because of this, other paramaters like base stats and IVs affect the amount of EVs needed to get an extra stat point. (You can understand why this is if you think about all the moving parts in the stat calculation formulae, and how the game chops off decimal points.)
There is no hard-and-fast rule to tell you whether Poke Pelago EVs will increase a level 1 Litwick's stats; but you can rest assured that they are considered in the calculation of its stats. Most of the time, investing all 252 EVs into a level 1 Pokemon's stat will be enough to increase it by 1 (and sometimes, as few as 4 will be enough!) but this is obviously subject to the maths. Whatever combination of factors gets you above the next integer is good enough.
Also, because stats are constantly recalculated by the game using an unchanging formula, it doesn't matter when your Pokemon gains EVs -- they'll have the same impact on your Pokemon's stat total so long as all other variables e.g. level, base stats, IVs and nature are the same. So a level 50 Litwick EV trained at level 1 is no different to another level 50 Litwick EV trained at level 50, assuming all its other attributes are the same.
Do not feel bad if this is hard to understand or if it's all a shock to you. Most resources online rely on simple explanations of EVs that work for the majority, but leave inquisitive people like you with more questions than answers.