The most accurate response to why Theodore Roosevelt thought merely the threat of force was sufficient to achieve his foreign policy goals is:
Recent military successes had established the U.S.'s ability to back up its threats.
Roosevelt believed that a strong military presence and the credible threat of force could be an effective means of achieving diplomatic objectives, reflecting his view famously summarized in the phrase "speak softly and carry a big stick." The idea was that by demonstrating military strength, the United States could influence other nations' behaviors without necessarily resorting to direct conflict.