Most employers prefer to hire through training or credential programs. You can find a welder apprenticeship through an employer and learn on the job. Some employers are willing to hire inexperienced entry-level workers so they can train them.
For entry-level welders, formal, technical instruction can last several months. You can also get welder-related training at a community college or technical school in the areas of math, metallurgy, physics, mechanical drawing and blueprint reading.
That's a short window for training for a secure job, and it sure beats the potential debt and time commitment of a four-year degree.