Trying to delay CABasicAnimation position and opacity of layer by 3 seconds but

The problem is that you're setting the boxLayer properties of position and of opacity to their end values. You need to:

1. Set the boxLayer properties to their starting values, not their ending values (this is why it's starting in the ending position/opacity ... usually if the animation starts immediately, this isn't an issue, but because you're deferring the start, using the ending positions is problematic);

2. For your two animations, you have to change removedOnCompletion to NO and fillMode to kCAFillModeForwards (this is the correct way to keep it from reverting back to the original position upon completion).

Thus:

// Create an animation that will change the opacity of a layer
CABasicAnimation *fader = [CABasicAnimation animationWithKeyPath:@"opacity"];

// It will last 1 second and will be delayed by 3 seconds
[fader setDuration:1.0];
[fader setBeginTime:CACurrentMediaTime()+3.0];

// The layer's opacity will start at 0.0 (completely transparent)
[fader setFromValue:[NSNumber numberWithFloat:startOpacity]];

// And the layer will end at 1.0 (completely opaque)
[fader setToValue:[NSNumber numberWithFloat:endOpacity]];

// MAKE SURE IT DOESN'T CHANGE OPACITY BACK TO STARTING VALUE    
[fader setRemovedOnCompletion:NO];
[fader setFillMode:kCAFillModeForwards];

// Add it to the layer
[boxLayer addAnimation:fader forKey:@"BigFade"];

// SET THE OPACITY TO THE STARTING VALUE
[boxLayer setOpacity:startOpacity];

// Create an animation that will change the position of a layer
CABasicAnimation *mover = [CABasicAnimation animationWithKeyPath:@"position"];

// It will last 1 second and will be delayed by 3 seconds
[mover setDuration:1.0];
[mover setBeginTime:CACurrentMediaTime()+3.0];

// Setting starting position
[mover setFromValue:[NSValue valueWithCGPoint:CGPointMake(startX, startY)]];

// Setting ending position
[mover setToValue:[NSValue valueWithCGPoint:CGPointMake(endX, endY)]];

// MAKE SURE IT DOESN'T MOVE BACK TO STARTING POSITION   
[mover setRemovedOnCompletion:NO];
[mover setFillMode:kCAFillModeForwards];

// Add it to the layer
[boxLayer addAnimation:mover forKey:@"BigMove"];

// SET THE POSITION TO THE STARTING POSITION
[boxLayer setPosition:CGPointMake(startX, startY)];

---

Personally, I think you're doing a lot of work for something that's done far more easily with block-based animation on the view (for the purposes of this demonstration, I'm assuming your boxLayer is a CALayer for a control called box). You don't need Quartz 2D, either, if you do it this way:

box.alpha = startOpacity;
box.frame = CGRectMake(startX, startY, box.frame.size.width, box.frame.size.height);

[UIView animateWithDuration:1.0
                      delay:3.0
                    options:0
                 animations:^{
                     box.alpha = endOpacity;
                     box.frame = CGRectMake(endX, endY, box.frame.size.width, box.frame.size.height);
                 }
                 completion:nil];

For using beginTime you should make necessary configuration of your animation object and set fillMode to kCAFillModeBackwards like

zoomAnimation.fillMode = kCAFillModeBackwards;

That's said in Apple documentation:

Use the beginTime property to set the start time of an animation. Normally, animations begin during the next update cycle. You can use the beginTime parameter to delay the animation start time by several seconds. The way to chain two animations together is to set the begin time of one animation to match the end time of the other animation. If you delay the start of an animation, you might also want to set the fillMode property to kCAFillModeBackwards. This fill mode causes the layer to display the animation’s start value, even if the layer object in the layer tree contains a different value. Without this fill mode, you would see a jump to the final value before the animation starts executing. Other fill modes are available too.

https://developer.apple.com/library/content/documentation/Cocoa/Conceptual/CoreAnimation_guide/AdvancedAnimationTricks/AdvancedAnimationTricks.html#//apple_ref/doc/uid/TP40004514-CH8-SW2

Also, from Rob's answer:

For your two animations, you have to change removedOnCompletion to NO and fillMode to kCAFillModeForwards (this is the correct way to keep it from reverting back to the original position upon completion).

It's a kind of controversial statement, because:

Once the animation is removed, the presentation layer will fall back to the values of the model layer, and since we’ve never modified that layer’s position, our spaceship reappears right where it started. There are two ways to deal with this issue:

The first approach is to update the property directly on the model layer. This is the recommended approach, since it makes the animation completely optional.

Alternatively, you can tell the animation to remain in its final state by setting its fillMode property to kCAFillModeForwards and prevent it from being automatically removed by setting removedOnCompletion to NO. However, it’s a good practice to keep the model and presentation layers in sync, so this approach should be used carefully.

From https://www.objc.io/issues/12-animations/animations-explained/

This article explains well why you shouldn't use removedOnCompletion with fillMode https://www.objc.io/issues/12-animations/animations-explained/

In my case I'm animating the layer of a view that functions as a navigation but delaying a bounce animation that is inside that view ; I NEED BOTH OF THESE POSITIONS UPDATED ON THE LAYER since it can be dismissed and then shown again. Using removedOnCompletion will not update the layer's value once the animation completes

The way I do it is update the layer in a CATransaction completion block

CATransaction.setCompletionBlock { 
     // update the layer value
 }

CATransaction.begin()

// setup and add your animation

CATransaction.commit()