If it's remote, it's on another server. This means you will need to connect to it somehow, whatever the solution. A usual solution is to just SSH:
ssh remote.server /bin/bash -c 'cd /path/to/remote/repo && git log --all -1 --format=%cd'
Some usual production UIs have rest APIs you can use etc. For Github for example, you can fetch the latest commit object with
https://api.github.com/repos/<user name>/<repo>/commits/<brancH>
(This is based on How can I get last commit from GitHub API) and parse the Json (or Yaml I don't know what they have now, Json seems enough) - under auther and commiter there are dates. If you don't know which branch has the latest commit you have to check them all.