If you want to work in a "big data"-type role as a developer, I wouldn't worry about finding huge data sets. There's a dearth of candidates, especially ones who actually have hands-on experience, and having deep knowledge of (and a little experience with) a broad range of tools will make you a pretty good candidate: Fire up a VM with a single-node install on it [1] and just grab any old CSVs. Load them into HDFS, que…
This is sadly true, for now. I don't think folks here disagree with the "true" part. Let me explain why it is "sadly" and "for now".
The biggest issue with big data is most of it sits unused. In many organizations, HDFS ends up being an alternative to NetApp storage servers, storing terabytes of data with the hopes of them being useful one day.
In fact, if you already get to that stage of using HDFS as a storage server, you must have a decent ETL team that can put data into HDFS with a menacing combination of ad hoc scripts and a workflow that looks like a cobweb produced by a deranged spider. For now, knowing the ins and outs of various semi-functional open source components and the tenacity, patience and skill to deal with the gnarliest of ETL tasks get you a high-paying data engineering job.
But, in the long term, there will be a big change.
1. Tools are getting better: many data practitioners are realizing there are huge gaps between different data infrastructure components, and they are trying to fill these gaps. There is a lot of attention given to query execution engines (Presto, Impala, Spark, etc.) but I find data collection/workflow management tools are just as critical (if not higher leverage) right now. Tools like Fluentd (log collector) [1], Luigi (workflow engine) are OSS software in this direction.
2. Data-related cloud services are becoming really, really good: huge kudos to services like AWS, GCP, Heroku (through Addons). They are quickly building a great ecosystem of data processing/analysis/database components that frankly work better than most self-administered OSS counterparts. (Disclaimer: my perception might be colored here since I work for a data processing/collaboration SaaS myself [3])
So, back to the question. I think aspiring data engineers have two distinct career paths:
1. Becoming an expert in a particular data engineering component: this would be building a query execution engine, designing a distributed stream processing system, etc. (It would be awesome if you decide to release as open source)
2. Becoming an expert on quickly and effectively deploying cloud services to get the job done: this is the skill most desired among data engineers at startups.
What not to become is one of these OSS DIY bigots: not good enough to build truly differentiating technology, but adamant about building and running their own . These folks will be wiped out in the next decade or so.
[1] https://www.fluentd.org [2] http://luigi.readthedocs.org [3] http://www.treasuredata.com