There's no guarantee you'll even get an algae bloom, or a diatom bloom or a bacterial bloom, but then it is possible and some new tanks go through more than one. As for timing, that's near impossible to pin down other than to say sometime after your tank is cycled and before 2 to 6 months. IMHO it's likely sooner rather than later. And it depends on so many factors. How did you cycle the tank?, Does your tank have livestock in it now, and what kind of livestock, and how much livestock? Are you feeding the livestock and how much? Are you doing water changes and how big a percentage of the water gets changed? You get the idea, right? There are just too many variables.
The good news is that none of the blooms is permanent and over the course of a week or two they usually go away pretty much on there own. The reason for the bloom is because there is too much of 'something' in your system and nature will find a way to get it used. But once the algae or bacteria start to use it, it will start to reproduce, and reproduce some more, and some more, and so on and so on. Finally it will reproduce to the point that there isn't enough of whatever it's using for food and the bloom will die back and almost go away. It may not go away completely as it will always be there to use up whatever small amount of that food was that it uses. But it shouldn't be so much that you see it as a problem. Sometimes it will , in fact, use up all the food, and if you aren't adding more (through feeding, or something in your water changes or whatever) it may go away completely.
A small amount of CUC or even a fish or two aren't a problem during the bloom. In fact algae eaters can be useful. But don't add corals until the tank is more stable. Corals don't tend to do well with algae blooms or diatom blooms or bacterial blooms. They don't like the water parameter changes and they don't like getting a coating of algae. Fish, hermit crabs, snails can all deal with it better.
Keep asking questions and good luck... oh, and welcome to the addiction!