Found the same issue here: https://answers.ea.com/t5/Technical-Issues/Apex-Legends-Stuck-at-loading-screen/m-p/12984421
I have tried running the game as Administrator and followed the below:
Step 1: Go to the installation folder of your Apex Legends to find the file named r5apex.exe and open its Properties.
Step 2: Under the Compatibility tab, check both Run this program in compatibility mode for and Run this program as an administrator options, and save settings.
Step 3: Launch Apex Legends and wait for the Continue button appears on the screen.
Step 4: At the bottom of the screen, click the Data Center option and then choose another suitable server.
Having done this the issue is still unresolved.
I also have 175GB free on my SSD so it's not a space issue.
Help on this issue will be much appreciated.