Try deleting the Origin client and re-download the latest version here: https://www.origin.com/usa/en-us/store/download
Right-click on the game before you launch it and select "Repair."
Try rebooting your network. If you're familiar with port forwarding we have the port numbers listed for Apex Legends below. Try rebooting the network first though to see if a simple refresh of the connection addresses this.
Basic Connection Troubleshooting
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