Characteristic impedance is set by four things: track width, dielectric thickness to the reference plane, the dielectric constant of the material, and the copper thickness. Three of them are ours; the first one is yours. Which is why an impedance-controlled job is always a conversation about the stack-up before it is a production order.
What we do in practice is take your target impedance and layer assignment and calculate the stack-up backwards — adjusting dielectric thicknesses and, where necessary, proposing a corrected track width. You get the calculated stack back for approval before tooling. A design routed to a guessed width and then declared impedance-controlled is the single most common source of failed first articles.
