What evidence does out Galaxy provide that Dark matter exists

Our galaxy rotates. Based on the matter we can detect within it, there's not enough mass to keep it from flying apart because of that rotation unless there's some other form of undetectable matter (dark matter) present to hold it together.

At that spin rate (measurable) and that much visible matter (measurable to a reasonably accurate level) there has to be something else holding the galaxy together.

Extended rotation curve.

Kinematics of nearby stars perpendicular to the disk of the Milky Way.