Be a happy camper?
Now, seriously, this is a case where the answer is: do nothing. Providing a visual cue to your users that your server is blazing fast is nothing to be ashamed of. Quite the contrary, it's a great indication for your users.
Besides, if you load the animation on a slow connection, let's say you have incredibly different time ranges going from 0.1ms to 1 second: why should the behavior be different? It's not different from 59 seconds 900 milliseconds
compared to 1 minute
, so the same should happen if the load takes 100 ms, 200ms, 500ms, 1 second, .... (N)
However...
If you really think it's an issue, I'd recommend testing with real users and see what's their opinion. Assuming it's a real issue (or it just annoys you) you can simply show the animation after some threshold time, which may be defined by you arbitrarily, or might be taken from testing results. Thus:
if {$annoyanceThreshold => true} : $noAnimation
else : $showAnimation;