Let me rephrase that for you. "Was there every a time when non-Sunni's were the largest Muslim sect?"

The reason I rephrase your question is that "Sunni" isn't necessarily the most accurate term to use. Certainly, I don't believe any of Muhammad's companions would refer to themselves as "Sunni". That term crystallizes later. In general, recent scholarship favors the term "proto-Sunni" to refer to the mainstream traditionalists in the early era of Islam (at least from a theological view). The boundaries of Sunnism as outlined in the seminal work Aqeedah at-Tahawiyyah were actually in (at least somewhat) flux in the early century or two. People as important in Sunni theology as Nu'man ibn Thabit (Abu Hanifa) held views that are not strictly "Sunni". In particular, his ranking of Ali as third highest of Muhammad's companions and not number four. Also some of the views on the issue of what constitutes belief, where some proto-Sunnis had views shared with the Murji'ah and even the Khawarij. These issues didn't really coalesce into a unified theology known as Sunnism until quite some time.

To address the intent of your question rather than nitpick though :-). Yes, mainstream traditionalists were always the largest sect. Groups believing in an esoteric knowledge carried by Muhammad's family (aka proto-Shi'as crystallizing into the Zaydis, Imamis, and Isma'ilis) were never the majority.

I'd recommend reading The Roots and Achievements of the Early Proto-Sunni Movement: A Profile and Interpretation by Matthew J. Kuiper for more about the issue of proto-Sunnis.