Trade deficit has been known to economists as a farce for decades, so no, they are not the only source of growth.
Most GDP of first world countries comes from services, not goods, which are not accounted for in “exports”.
Once again, if a clickbait title asks a question, the answer is “No”. Otherwise, the title would be the much stronger affirmative statement, e.g., “Exports are the only source of growth for countries”.