Can I download the Spectrum TV app on a 1st gen Apple TV?

The Spectrum TV app is compatible with

• Apple TV HD (4th generation) (tvOS 13 or later) (2015 model)
• Apple TV 4K (1st generation) (tvOS 13 or later) (2017 model)
• Apple TV 4K (2nd generation) (tvOS 13 or later) (2021 model).

It is not compatible with Apple TV (3rd generation or earlier) (2007/2010/2012 models).

no, only appletvs that support an app store are appletv hd(4g) appletv 4k(5g) and appletv 4kse(6g)

also you proably don't have the first generation they looks like this http://www.letemsvetemapplem.eu/wp-content/uploads/2013/12/apple_tv1.jpg