The inflationary paradigm has transformed our understanding of the early universe; yet most inflationary models are considered geodesically past-incomplete, suggesting a beginning of time or a primordial Big Bang singularity. The Borde–Guth–Vilenkin (BGV) theorem is often cited as demonstrating that all eternally inflating spacetimes must be past-incomplete. Utilizing a new theorem establishing geodesic completeness in generalized cosmologies, we present a simple, explicit class of inflationary