Attaching to an actor with an Animation

I am looking to have a character attach to a Vehicle or Mount. The idea is the character plays an animation to get on or get in the vehicle and then attaches to the vehicle (before or After) the animation plays.

The Animation being played is currently part of a montage. When the player gets on the mount there appears to be a “jump” in the position of the character. Currently the character attaches to the mount and then plays an animation of it getting in or on. The problem is the character “Jumps” to the attached position for one frame and then the mounting animation kicks in where the character is in the correct location to play the mounting animation.

Is there a way to get rid of this 1 frame jump? The logic of attaching the character and playing the animation happen as part of the same tick.

I have tried setting blend in and blend out to 0 which improved it slightly but the jump is still visible.