Use javascript in order to set the current percentage of a css animation

You can specify a negative animation-delay property.

Example: http://jsfiddle.net/vyhjt6mu/4/

In that example I've set animation-delay: -30s so the animation will start from the middle point

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For this task you could set 24 different classes in CSS (one for each hour) like so

.h00 {
  animation-delay: 0s; 
  -webkit-animation-delay: 0s; 
}

.h01 {
  animation-delay: -2.5s; 
  -webkit-animation-delay: -2.5s; 
}

.h02 {
  animation-delay: -5s; 
  -webkit-animation-delay: -5s; 
}

...

.h22 {
  animation-delay: -55s; 
  -webkit-animation-delay: -55s; 
}

.h23 {
  animation-delay: -57.5s; 
  -webkit-animation-delay: -57.5s; 
}

where the difference of delay between each hour is 2.5 seconds (60s/24); then, via JS, get the current hour via getHours() method and apply the right class name to your element