Although the classical and alternative routes of complement begin with completely different recognition events, they are engineered to funnel into a single shared terminal sequence, and the question asks where that merge first occurs. The classical arm uses $C1$ to sense immune complexes and then recruits $C4$ and $C2$ to build its convertase, whereas the alternative arm bypasses $C1$, $C4$, and $C2$ entirely and assembles a separate convertase directly on microbial surfaces. The crucial design feature is that both convertases, despite their different make-up, exist for one purpose: to split $C3$. Once $C3$ is cleaved the two streams become indistinguishable and proceed together through $C5$ and on to the membrane attack complex. Thus the earliest molecule common to both pathways is the third component of complement. \[\boxed{C3}\]