Line-intensity mapping is a promising probe of the Universe's large-scale structure. We explore the sensitivity of the DSA-2000, a forthcoming array consisting of over 2000 dishes, to the statistical power spectrum of neutral hydrogen's 21 cm emission line. These measurements would reveal the distribution of neutral hydrogen throughout the near-redshift Universe without necessitating resolving individual sources. The success of these measurements relies on the instrument's sensitivity and resilience to systematics. We show that the DSA-2000 will have the sensitivity needed to detect the 21 cm power spectrum at z ≈ 0.5 and across power spectrum modes of 0.03–35.12 h Mpc−1 with 0.1 h Mpc−1 resolution. We find that supplementing the nominal array design with a dense core of 200 antennas will expand its sensitivity at low power spectrum modes and enable measurement of Baryon Acoustic Oscillations. Finally, we present a qualitative discussion of the DSA-2000's unique resilience to sources of systematic error that can preclude 21 cm intensity mapping.