I don't follow this logic. If you're using minimum force and the other side is numerically superior and using maximum force, you are basically setting yourself up for defeat.
I think that Russian plan honestly expected the Ukrainian resistance to collapse within days and the Russian soldiers to be welcomed as liberators. They sent token forces deep into Ukraine expecting that the local populace would overthrow the local government at the first sight of the Russian liberation army. It was quite obvious that their orders in the opening days was to be as gentle as possible.
Russia committed 120 of its battalion tactical groups to Ukraine out of about 170. BTGs are the core of the ground forces, which are not that large at 280,000 active duty in total. They also have about 45,000 Airborne troops, 12,000 naval infantry and an undisclosed number of SOFs.
Ukraine started the war with about 200,000 active duty soldiers, bolstered by a paramilitary force at least 100,000 strong. They have been mobilizing for a full month now and thanks to a deluge of small firearm supplies arriving from the West they won't be running into a problem equipping those troops anytime soon. From what I've been able to gather they've already mobilized an additional 150,000 troops. The war has entered a phase of attrition and it's not looking good for Russia right now.
