It is not being wise after the fact to point out that this event was mis-handled as soon as the aircraft is airborne.
Liftoff is at 05:38:39
L/H stickshaker activates almost immediately. ( Birdstrike?)
Captains first attempt to engage autopilot is at about 400 ft AGL.
It doesn’t engage but after several attempts appears to have engaged till just after flap retraction at 05:39:45
MCAS cannot have been an issue till then, 1:06 after becoming airborne.
Engaging an autopilot with stickshaker active at 400 feet is a seriously bad idea.
It is not second guessing to say that at that point flying an attitude and thrust setting would have been the wisest option.
Startle factor is huge. I’ve been there. But that’s where you justify your pay check.