Battles with neutral creatures.

Sounds about right. That's how I've been doing it. It just takes a lot of time – it felt faster in Heroes 3. The only thing that helps is that the AI is dumber – after a month of tough battles and losses, when you finally reach an open area, the AI hasn't cleared its entire territory yet, whereas in the third game, it would have already taken half of yours.
By the way, a related question arose – what do you think is better: to quickly defeat neutral forces with significant losses, gaining experience, resources, and artifacts, but remaining with a small army before a strong enemy, or to build a larger army, defeat neutral forces with minimal losses, but lose resources, artifacts, experience altars, and time? The enemy's army will also grow during this time.