The most likely reason the timer will not start is that the checkdiskspace.timer should be configured to allow manual starts. By default, systemd timers do not allow manual activation via systemct1 start, unless they have RefuseManualStart=no in their [Unit] section. This option prevents users from accidentally starting timers that are meant to be controlled by other mechanisms, such as calendar events or dependencies. To enable manual starts for checkdiskspace.timer, the administrator should add RefuseManualStart=no to its [Unit] section and reload systemd.
The other options are not correct reasons for the timer not starting. The checkdiskspace.timer unit does not need to be enabled via systemct1 enable, because enabling a timer only makes it start automatically at boot time or after a system reload, but does not affect manual activation. The timers.target does not need to be reloaded to get the new configuration, because reloading a target only affects units that have a dependency on it, but does not affect manual activation. The checkdiskspace.timer does not need to be started using the sudo command, because the administrator is already running systemct1 as root, as indicated by the # prompt. Reference: systemd.timer(5) - Linux manual page; systemct1(1) - Linux manual page