DGX Spark is an ARM64 host system. Although SDK Manager itself can be installed on ARM64 Ubuntu hosts, the supported host OS for each SDK package is defined separately by the SDK package compatibility matrix.
For JetPack 7.x, the SDK Manager compatibility matrix does not list ARM64 Ubuntu as a supported host for JetPack flashing. The JetPack 7.x row lists Ubuntu 22.04 / 24.04 host support, but the ARM-specific Ubuntu column is not enabled for JetPack 7.x.
Because of this, DGX Spark with Ubuntu 24.04 ARM64 is not a supported/validated host configuration for JetPack 7.x Direct Flash, so SDK Manager may not show the Direct Flash option in this environment.
Recommendation:
Use SDK Manager Direct Flash from a supported Ubuntu x86_64 host, such as Ubuntu 22.04 or Ubuntu 24.04.
If a USB installation drive is available, use the documented Jetson ISO installation method.
Since you mentioned that a USB flash drive is not an option, the supported path would be to use a supported x86_64 Ubuntu host for Direct Flash.
Please refer to the SDK Manager compatibility matrix and Jetson Thor BSP setup guide: