Googler opinions are my own. I know little about BQ.
My understanding of Big query is that at least some of the tech it's based on allows for handling very large datasets. I'm talking being able to search BI that is petabytes in size. I don't think it's really designed for small datasets.
If you can stick the data in SQLite, I think you're using the wrong tool.
Searching around, it looks like BI Engine may help in cases like this. See: https://cloud.google.com/blog/topics/developers-practitioner...