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 sample(s) or give you a problem statement and ask for a code sample.
Anymore employers are going to want code samples especially with little experience. Create a github and post a couple code samples that show off your strengths.