get to Industrial age first. most times they go first
Which you can sometimes turn to your advantage.
Example:
One of my favorite GE encounters occurs in Contemporary Era. It is the one with a two wave enemy army. First wave consists of 4 Missile Artillery and 4 Anti-Aircraft Vehicles. Second wave is Missile Artillery and Machine Gun Teams. I love to attack it manually with 8 Attack Helicopters. The Attack Helicopters move first, and the Missile Artillery can't hit flying units. So I take out the AAVs first, gladly suffering their return fire on 4 of my units, then hit auto to mop up the artillery. Same with second wave, hit the MG Teams first manually then mop up the artillery on auto. Guaranteed no lost units.
If you don't like taking damage before you can surrender or hit the enemy yourself, use Rogues to your advantage.
Example:
Another Contemporary Era GE encounter (actually a couple near the end of level 4). Enemy consists of two waves, both waves with 4 Missile Artillery and 4 Assault Tanks. I use 1 Attack Helicopter and 7 Rogues. Move the AH back one tile, then let the enemy units move. The ATs may transform one or two of your Rogues, and the artillery will probably transform all the rest without damaging your real AH. Then you take out at 2 of the ATs and damage a third, keeping your real AH as far as possible from the two remaining. You may actually lose one AH on their second turn, but that's fine as long as it's not your real one (which is why you keep it farther from the remaining ATs). Then finish off the other two ATs on your second turn before hitting auto to mop up the artillery. Same exact tactic for the second wave. Guaranteed win with minimal unit loss.
So that's at least 3 encounters (there are many more) just in Contemporary GE where you turn either the first move strike ability or the Rogue's special ability to your advantage, or both.