"Our cats eat eggs."
Translation:Наши кошки едят яйца.
I think that it would mean "of our cats" https://en.wikipedia.org/wiki/Grammatical_case#Russian
Counter-question: Why do you feel there should be a preposition at the beginning? It would help to understand your thinking to give a more direct answer.
This is a pretty straightforward translation of the sentence in either language, where you have Subject - Verb - Object.