Simultaneously: If you want to express that something happens at the same time.
At the same time: A more informal version of "simultaneously."
Concurrently: A more formal version of "simultaneously."
Immediately: If you want to express that something happens right after.
Later: If you want to express that something happens after a period of time.
Beforehand: If you want to express that something happens before another event.
Subsequently: If you want to express that something happens after another event.
The best antonym for "meanwhile" will depend on the specific situation and the meaning you want to convey.