It's company-specific.
I previously worked for a large aerospace company. Associate {Discipline} Engineer was the lowest level, typically a recent college graduate with little to no internship experience. {Discipline} Engineer was the next level and was where college graduates with some experience were hired. And from there, you would progress up to Senior and Staff and Principle. There were also grades (I, II, III) within each level for some more granularity, but those were almost exclusively pay and not role or responsibility changes.
The grade of "Staff" also varies, and is a good example. At that employer, a Staff Engineer was more experienced and held more responsibilities than a Senior Engineer. However, a Staff Accountant is usually a lower ranking position than a Senior Accountant at many companies, from colleagues who work in finance and accounting.
However, at your company, it seems like Associate is more than an entry-level or junior position, since it's something you are aspiring toward.
You should consult with your manager during a 1:1 session about your career growth and understanding what the criteria is for the next level and what you can do to demonstrate the ability to take on more responsibilities.