This would be similar to pushing a, say, 100m stick against a concrete wall since the inertia of a stick multiple LYs in length would be comparable. Sure, you could push the end 10cm, but it would just crumple or bend.

Fun with math: If the 'stick' was a steel rod about a cm square, it would weigh around 7,400,000,000,000 tonnes per light year. That's only 1/10,000,000th the weight of the moon, but it's still substantial.