I think you are making too much of:

> Typically, they ask for a applicant's github profile or equivalent
> open-source project profile for evaluation.

I don't take that as they expect an open-source project or even a github profile.  They would like codes samples from you and want to know if they are available.

If you don't have code samples then they will either need to forego code samples or give you problem statement and ask for a code sample.