How to take the next step?

Summary

Going on 1YOE as a data scientist at a small consulting company. Have a STEM degree but no masters. Current role is as a contractor, so around full time work, but I am looking to transition into something more stable. Is making the jump to a bigger companies DS team possible without a masters? Feels like thats the new baseline. Not super excited about going back to school, but had no luck applying to other positions. I went to a great university but its not American, so little alumni network ...