I think you are over-estimating the average Ukrainian's desire to fight.
From what I hear, they have been dodging conscription en masse.
Chances are the majority of them will just move to the rump state to the west or go back to civilian life.
You don't need the average person to fight, or to be willing to fight.
What you need is a relative handful of people willing (and equipped) to fight and then a general population that is neutral in those fighters favor.
You need locals willing to tell the fighters where Russian forces are and locals unwilling to tell the Russian's about the fighters sitting out in the woods.
A sniper sits around and then takes a pot shot at an officer, then they dissapear. If a Hind, for example, gets called in to engage them then the guy with a Stinger takes his own pot shot and disappears. A tank is moving? Then someone uses a Javelin to wreck it before fading away.
A town has a few dozen Russian troops occupying it. Well one day they find themselves set upon by a hundred guerillas who kill them all and then fade away into the general population.
The hardest part of truly effective/painful insurgency is getting resources. Well if, with the willing help of the Ukrainian government, the US provides entire container ships of not just small arms but secure radios, satellite phones, small drones, C4, night vision, body armor, etc. and has all of that broken up into small supply caches spread across the whole of the nation then suddenly the hardest part of effective insurgency is taken care of.
And lets not get into the (almost certain) US deployment of deniable trainers for those future insurgents. One of the core purposes of the Green Berets is training insurgency forces.
You think Iraq or Afghanistan were bad? What do you think happens when the US is feeding intelligence information, including satellite surveillance and ELINT, to the insurgents on the ground and has the entire US propaganda ecosystem spinning the insurgents as the good guys. Russians massacre a village, for example, and suddenly it is being streamed on CNN in full color 1080p.
Funding? Well those insurgents will basically have limitless foreign funding. Less useful inside of the area given the sanctions and how isolated the area is/will be but still very useful.
It's cute you think Russia has any chance of actually sealing the borders.
At scale? They absolutely do. The US, right now, could fly an entire C-130 filled with - for example - Javelins into Poland, load them onto a truck, and then just drive them into Ukraine via a major highway.
Stopping THAT kind of thing is what Russia is initially worried about.
Or the "here's twenty million rounds of crated 5.56 and ten thousand M16A2's complete with underbarrel grenade launchers and a few hundred grenades each" shipments.
Where Ukraine can take all of those small arms and then just go town to town and say "Free weapons and ammo for everyone who wants some" and let all of that hardware just walk away, deliberately untracked and untraced, with the locals to be hidden away as and how they will.