Yeah you can win without tanks ( especially vs the AI 9. You probably want something that can do damage though, like CAS / Artillery or both, and be ready to take more casualties.
Let's take an extreme case like a width 40 infantry div consisting of 20 inf battalions without CAS support, i.e. the Chinas.
Only benefit: infinite manpower.
You can't hold lines pretty well with enough of those divs. A little tough against tanks, but with plenty of rotation, doable.
On the offensive you can hardly push a hole into the enemy lines. This is where micro enters the fray. Make sure to have a battleplan set up which you never execute. You just need the bonus.
The rest is timing: there will always be times when the a.i. has exhausted itself and you can counter-attack some adjacent provinces where the enemy is currently on low org. Other opportunities are temporary local superiority where you can mass all neighbouring infantry to concentrate an attack on a single province.
Ideally you utilize these micro attacks in a pattern that lets you slowly advance towards a pocket.
PS: Just because you are the invader doesn't mean that you have to do the attacking. Pure infantry can work, especially if you can afford CAS and the use of strong templates with arty and breakthrough.