Both SpaceX and Blue Origin are planning to send demo landers to the moon, before their crewed missions for Artemis III and V respectively.

Even before the official uncrewed demo landing Blue Origin is planning to send two pathfinder landers to the moon, in 2024 and 2025.

These BO landers might not actually look like the Artemis mission lander. They will likely be the small "Blue Moon" landers, not the lander that got awarded the Appendix P contract. Nevertheless, these landers count for the purposes of this market.

Starship's uncrewed demo landing is scheduled for 2024, according to NASA's timeline.

Will Starship land on the moon before a Blue Origin lander does?

The landing doesn't have to be successful, as long as it physically hits the moon.