Yes, I think it is possible if you are a good student and perhaps have interned with a unit to get a job as a technician in a lab. However, I think it is much more common to have an advanced degree, especially for job advancement in the future.
A bachelor's is a common degree for entry-level forensic scientists. With an advanced degree, it's easier to advance to higher ranks plus helps if you are interested in management positions. At the crime lab I'm interning at, most people started (and still have!) only a bachelor's. Some have received their masters after being employed.
Like I've seen people post in other discussion, it is all about weighing the pros and cons of getting the advanced degree, if you're interested.