Pronunciation (Received Pronunciation, General American) IPA(key): /ˈtsaɪtˌɡaɪst/, /ˈzaɪtˌɡaɪst/
https://www.merriam-webster.com/dictionary/zeitgeist also gives two: ˈtsīt-ˌgīst ˈzīt-
I tried to get statistics from listening to https://youglish.com/pronounce/zeitgeist/english? but found I have a hard time distinguishing the two forms.