You need to make contact with new regions and stop making missions in regrion where vigilance is too high.

More vigilance means more troops and eventually retaliations.

Ok so, after learning about infiltration, it makes the missions way easier.

You need to choose what to rush research on.
No way should the enemy be any challenge if you rush lasers then mag weapons. The enemy will still be on its first phase, even before Chosen turn up.

I always go for mag weapons, using Hazmat suit and Predator armor until I unlock advanced mag weapons which unlocks Elerium , then coils which unlocks plasma weapons and power suits

Choose either Sparks or Psi Ops lab ( not both ) use the Proving grounds for research but forgo all MEC related stuff, or forgo Psi and focus on Spark MEC units.

Psi Ops are cool, but it does require a slight pause on base building as you will need to build a power supply.

Liberate first 2 sectors ( contacts early ) .. Just do the missions that unlock it. Then run the destroy network using a Reaper a sniper and a couple of assaults.~ Run your Reaper around as spotter and kill at range for 2 rounds then retreat, rinse and repeat.

If you carefully rush the research you want, and just use basic armors,
Buy the first engineer and scientist at black market, generally you can set yourself up to be quite offensive running 4 man teams early game.

This all needs to be in place before June?
The missions will tell you how many enemies.
By the time I had lasers, the enemy still were just grunts, and by mag weapons , enemy MECS had only just started showing up.
I also run missions to lower enemy strength in areas.
If a mission is just a boring snatch and grab, I normally pass on it.
Only doing ones that help me liberate or gain soldiers/engineer/scientist