Smooth camera movement

I want to smoothly move my camera from some point to main character when game starts but as I use deltaTime which can get pretty big values on start this movement appears to be very very quick. If I pause game on first frame and then click play everything gets right as some slow calculations are already finished. So I need some good way to wait until start calculations are finished. I tried smoothDeltaTime but it is not very accurate to.

There is a script in Components called Smooth Follow.
And maybe you should move some code from Start to Awake.