We derive a mechanism for the Hubble tension in which spacetime is modelled as a self-oscillating scalar field in a non-zero ground state. The 9% discrepancy between CMB-inferred (67.4 +/- 0.5 km/s/Mpc [1,2]) and locally measured (73.0 +/- 1.0 km/s/Mpc [3]) values of the Hubble constant arises because each measurement probes the universal oscillation at a different phase angle. The dimensionless background amplitude A = 1/2 is derived as a topological invariant from the Dirichlet boundary condition at the causal horizon, eliminating it as a free parameter. Taking the early- and late-universe H_0 values as observational inputs with no additional fitted parameters, the resulting nonlinear coupling constant lambda = 2.24 is O(1) and satisfies naturalness. The t(z) relation is computed self-consistently from the modified Friedmann equation, yielding H(z) predictions at intermediate redshifts testable by DESI, Euclid, and the Vera C. Rubin Observatory within five years. A further consequence is that the Hubble tension is time-dependent, oscillating with period T ~ 93 Gyr -- a prediction with no analogue in LCDM. The cosine phase dependence of the H(z) curve naturally mimics the time-evolving dark energy equation of state (w_0 > -1, w_a < 0) recently favoured by DESI DR2 [5,6]. Keywords: Hubble tension, oscillatory spacetime, topological amplitude, Dirichlet boundary condition, naturalness, anharmonic oscillator, self-consistent Friedmann equation, dynamical dark energy