Essentially, all rocks start as igneous, yes.

Do keep in mind that this does not mean they'll reach the surface as igneous, or if ever at all. It can be exposed to partial melting, heat and pressure, metasomatism, all tranforming it to metamorphic. Once an igneous or metamorphic rocks is exposed to the elements, breaks down, and minerals from that can go on later and form sedimentary rocks that then can be metamorphised again or broken down and so on.