No, it was not the only one, but 19th century models were purely speculative, Lewis did not publicize his 1902 cubical atom until 1916. So in 1904, when Thomson proposed his plum pudding, the only real competition was Nagaoka's 1903 Saturnian atom, a large, massive, positively charged sphere, encircled by hundreds of light-weight electrons arranged into flat rings, and bound by electrostatic forces (analogous to rings of Saturn). It was an inspiration for Rutherford's 1911 model, and shared the problem of all "planetary" models pointed out by Thomson: rotating electrons radiate energy according to Maxwell's theory, so the atom would promptly collapse. Nagaoka abandoned his model in 1908, and Rutherford's was saved by Bohr in 1913 using the new idea of quanta.
However, in 1909 Rutherford's scattering experiments that atoms have large empty space within them rather than Thomson's pudding filler, so we only have a span of five years for the plum pudding to stay accepted. It was more or less, as the best available offer and provisionally, and as such it motivated more experiments including Rutherford's. The model itself was provisional, Thomson was silent on what the pudding is made of, or what held it together. But there were similar issues with the electron at the time. In Maxwell's theory point-like accelerating charge has infinite self-interaction energy, so little ball electrons were considered by Abraham for example, and Poincare even conjectured a new non-electromagnetic attractive force to stabilize them. After Planck's and Einstein's discoveries the general sentiment was that physics is in flux, and little is settled.
Atoms were considered indivisible for most of 19th century, but Fechner speculated about "small suns, floating at comparatively large distances from one another, such that each or several of them together are surrounded by orbiting planetary atoms” as early as 1828 (he also suggested that electric current is a flow of corpuscles in 1845), and Weber proposed an atom with small positively charged mass rotating around a large negatively charged one in 1871. Weber based his model on his own version of electrodynamics, different from Maxwell's, so it became obsolete by 1890s. Stoney (who gave electron its name in 1891) also suggested a "planetary" model.
See Jagdish and Rechenberg, Historical Development of Quantum Theory for more details.