Hi there,
Have you had the chance to try repairing Apex Legends to see if that helps? If you're using Origin you can right-click on the game in your Library then select the Repair option when the menu pops up.
If you're using Steam try verifying the integrity of the game files to see if that helps. For more info on how to verify the files check out the Steam Support website. Once you've had the chance to give this a try please let me know if you're still having any trouble starting up Apex Legends.
Thank you!
/Kent