If you see an alpha rex please be careful, they are unbelievably scarier than a normal rex keeping up with a spinosaur and not getting phased by anything we threw at it. Rip Zeus, level 113, the rex was 25.
This is tge least threatening creature in the game once you hit lv 10. Craft a bow and some arrows, shoot it and kite. If it is gaining on you, run past a herbivore, it will lose aggro almost instantly. Keep shooting that sweet sweet early exp and possibly early metal tools.
To tame a Rex build a stone trap by placing foundations in a square or rectangle at least 8 by 8 then making 4 walls out of stone door frames 4 high (or you can use standard Dino gate frames for 3 walls, then put the door frames for the 4th wall). Then make a wooden ramp down one side of the trap (the ramp will attach to the top of the door frames). Once you have your little trap with a ramp get the Rex to chase you. Run up the ramp and make sure it’s right behind you, then jump into the trap and run out one of the door frames. The Rex will fall in and not be able to leave. Tranq it out through the open stone door frames or Dino gates from a safe distance away. Catch any level Dino with this trap. Bigger Dino’s need bigger traps.