You can't beat your foe early. The most you can do is focus on gaining resources, and for that, your very first troop, the light infantry, is the most economic.
After you gain enough resources (and your foe as well) they will start to throw out troops that oppose yours. The way around this is to predict that, and throw out counter troops.
Keep doing this until you get enough money that you can throw out high lords out the wazoo.
Congratulations. You've won.
I don't mean to make it sound so easy, considering I'm playing it on Hard; but the formula is an absolute. In fact, you can predict your wins and losses by a simple measure of who is reacting to who early on. Are you reacting to the computer? You've lost. It doesn't matter how long the game goes on for. You've lost. Is the computer reacting to you? Good job, you've won.
The actual difficulty in the game comes from knowing when the 'tip' happens, where it is more profitable to start putting out efficient troops to fight, rather than troops to boost your economy.
The computer knows this better than you do, so naturally it's going to win a lot more before you get the hang of it, but the formula remains.