The Short Version
The core assertion is well-supported: Filipino and American forces did advance through southern Luzon, including Cavite, toward Manila in early 1945 as part of the Luzon campaign. The 11th Airborne Division landed at Nasugbu Bay and pushed north, with Cavite liberated by combined American and Filipino guerrilla forces starting January 31, 1945. However, this was a secondary flanking operation—the primary thrust came from the north via Lingayen Gulf—and the claim's phrasing may overstate the scale and centrality of the southern corridor.