I have been experiencing the same problem since three days. apex legends crashes after 10-20 seconds on launch. it would show no error message and would just send me back to origin
Have you had a chance to try repairing Apex Legends in the Origin client to see if that helps at all? If you right-click on the game in the Origin Library you'll see a Repair option when the menu comes up.
Let me know if that helps at all with the crashes you've been seeing. Thanks!