Can I update an Apple TV (1st generation)?

To avoid confusion, please find the model number that starts with an A, followed by four numbers.

Identify your Apple TV model - Apple Support

Find your Apple TV model number - Apple Support

A1218, A1378, A1427, A1469, A1625, A1842, A2169, A2737, or A2843.

Apple TV 4K (1st generation) [A1842] from 2017–2021 can be updated to the latest version system software (tvOS 18.2 at this time).

Apple TV (1st generation) [A1218] from 2007 cannot be updated beyond the 2010 software release.

No

most likely not

Apple TV - Wikipedia

appletv 1g (2007) support up to Apple TV Software 3.0.2 (modified build of Mac OS X 10.4 Tiger)

appletv 2g (2010) support up to Apple TV Software 6.2.1 (based on iOS 7.1.2)

appletv 3g (2012) support up to Apple TV Software 7.9 (based on iOS 8.4.6)[168]

appletv 4g (HD) (2015) support up to tvOS 18.2 (based on iOS 18.2.1)

appletv 5g (4K) (2017) support up to tvOS 18.2 (based on iOS 18.2.1)

appletv 6g (4K 2g) (2021) support up to tvOS 18.2 (based on iOS 18.2.1)

appletv 7g (4K 3g) (2022) support up to tvOS 18.2 (based on iOS 18.2.1)