Searching for raw data requires different concerns than searching for more traditionally published research. Things you will want to think about:
Raw, unanalyzed data is not a source that communicates its point easily to others--that's why we analyze it. As such, most people are going to choose to share their point with data that has been analyzed in some way (statistics, tables, graphs and other visualizations). So one needs to approach the search for that data with this obstacle in mind.
Collecting data can be very expensive, in terms of hours, resources, and money. Therefore, you'll want to consider who would care enough about your topic to dedicate their time, resources, and money to doing so. Government agencies, grant funded academics, advocacy groups are all examples of folks who may be able to do so. Considering which specific groups might be applicable for your topic and searching for data they share may be as successful an approach as looking in a data repository.
They data you want may exist, but it may also be restricted or otherwise proprietary. A sports team, for example, may collect a lot of data about their players and how they perform, but they would use that data to get a leg up on the competition. Therefore, they are unlikely to share that information publicly.
Anonymity may also be a concern that leads to restricting access to data. Does your topic focus on children? Is it very recent? Does it deal with a smaller, easily identifiable population? A yes to any of those questions might lead researchers to restrict access to the raw data and only provide topline reports.
Sometimes you have to come at data from a different direction. If you see a paper or table that is appropriate for your topic, can you trace the source for where they got their data? Is that data publicly available?
You may be able to combine multiple datasets to create one that suits your topic. However, prior to doing so, you should consider things like the time period, population, and methodology of the data collected. Are they comparable? Will you be drawing false conclusions?
For this assignment, you already have a topic in mind. So before you dig right into searching, think about: