He doesn’t need to do much to prove them wrong.
Nothing he can do will prove anything. Big Tech and Finance owned media will just lie over and over again. They'll never stop. New York's actual socio-economic condition won't be reported on, except in the most polarized "everything is horrible, please liberate our people from the tyrannical Mamdani regime" light.
You will be mentally tortured for watching TV or using the Internet until he is removed from office.