You can schedule them slightly in the future.
var source1, source2;
var when = context.currentTime + 0.01;
source1.start(when);
source2.start(when);
That'll schedule both sounds to play exactly 10ms from the moment you define when
. It's quick enough that it'll be perceived as immediate, but gives a bit of breathing room for the overhead of actually calling start
on the first source node.
There are better ways to do this if you have a ton of nodes, but for simple situations, this should be fine.