Keep going to Chapter 3
You get your first gun in Chapter 3. If you have finished Chapters 1 and 2 and still have no firearm, continue to the next chapter.
The opening uses movement and kicks before introducing guns. An empty weapon selection at that stage does not mean you missed a gun in the first two chapters.
After the opening
Once armed, the default controls are left mouse for primary fire, right mouse for secondary fire, Q for the weapon wheel, and the mouse wheel to change weapons.
See the beginner controls or browse the weapon overview for what comes next.