The Buddhist monk suicides were to protest the Diem regime. Diem’s sister-in-law, Madame Nhu, the Dragon Lady, mocked them as “monk barbecues.” But they probably helped lead to the downfall of Diem in November 1963. That was when the US presence in South Vietnam was still relatively small.
But, it was already on the books to expand the U.S. presence in Vietnam and it did happen so.