In 2022, there were 178 successful orbital launches; SpaceX's Falcon 9 and Falcon Heavy rockets accounted for 61 of them, or 34% of successful launches.

In 2023, Falcon rockets accounted for 96 out of 211, or 45%.

Will SpaceX be responsible for over half of successful orbital launches in 2024?

This includes Falcon and Starship (and in theory other SpaceX rockets), and only counts successes. Resolution will be based on the Wikipedia counts as of ~ 2025-01-03, assuming they appear up to date and not in dispute. Resolution will be delayed if required.