is it possible to work your way from being a data analyst to a data scientist or data engineer ?

I'm currently pursuing my degree in computer science with a specialty in data analysis/ business intelligence and I want to be a data engineer or someday a data scientist but not now. I have successfully done many data-related task such as image recognition or OCR and my python / R skills are not shabby at all. Should I have gone for data science degree from the get go or is there still hope ?

analyst data data analyst data engineer datascience data scientist engineer work