Once varroa is present you will never rid the colony entirely. The best you can aim for is to keep the levels tolerable so that they don’t damage the colony.
It is possible to go treatment-free but that is an entirely separate consideration.
It’s important to understand how and when varroa levels are important. The single most crucial treatment, in my opinion, is in late summer/autumn after you have taken the honey for the last time and before winter bees are made (these are the ones that will take your colony through to spring).
They need to be as healthy as possible; they have a long time to live and much work to do when brooding starts anew.
After harvest is when the brood nest contracts and there comes a time when varroa will outbreed bees. You need to take action then.
There is a choice of using Thymol/Formic acid/Oxalic acid as the “non chemical soft options” or going for pesticides.
I personally fog oxalic after harvest. You don’t need the colony to be brood-less for oxalic to work. You just have to repeat the process every five days for three treatments. I fog from under the mesh floor from the back of the hive. The bees hardly notice.
Most people who use thymol or formic (MAQS, say) will dribble oxalic on the cluster mid winter. I personally think that if your autumn treatment was effective, this is unnecessary.
When the colony starts making drones I uncap a few to see the level of infestation and put in a short frame if there is a problem. The bees make drones which will take most of the varroa and you can cut it off after capping.
Artificial swarming will create a brood-less period further slowing varroa build up.
There are other methods of trapping the queen and sacrificing newly laid brood to remove varroa.
PS treatment free options include removing drone brood as explained above, letting the bees build their own comb. Some bees exhibit hygienic traits and have high levels of DWV type B which is asymptomatic and displaces the harmful type A which causes deformed wings. These bees seem to cope somehow on their own. Personally I don’t think you can go treatment free unless you are lucky enough to have this scenario or breed for it.