--When Aliens steal the Sun cause it's not Homesteaded - An Absurdity within the NAP--
Imagine aliens with advanced technology come to Earth's solar system and take the sun away. Earth stops receiving sunlight and thus freezes to death.

This is not a violation of the NAP, because humanity does not own the sun. The sun is not homesteaded, until the aliens homestead it. Humanity owns the sunlight as it reaches the Earth, but owning the sunlight that reaches our planet does not mean we own it's source.
 

--The Bird Cage Analogy--
Imagine there is an unowned cage. You place a light-bulb above the cage and turn it on. The light-bulb is your property.
Later, someone random third party brings their pet bird and puts it in the cage, and walks off. The bird is their property.

You come back and decide to turn your light-bulb off. You do.
The bird goes to sleep, gets cold, and dies in it's sleep.
Did you violate the third party's property rights over their pet bird? No, because withholding support is not the same as physical violation.

From this we can derive that if the sun was owned by aliens previously, they would have a right to turn the sun off.
Now imagine the aliens simply homestead the unowned sun. Does that actually change the situation at all? What if the light-bulb on the cage is unowned to begin with, and you simply homestead it by changing the bulb, and then later turn it off? Does that suddenly become aggression?
What if the bird owner abandoned the bird, and we assume aggression against animals is itself wrong? Does that turn this into a violation of the NAP? No?
The answer to all of this is no under the NAP. Dependency does not and can not grant entitlement. It isn't your fault the bird is in the cage, if you homestead the light-bulb it's yours, end of story.
 

--But stopping Sunlight from reaching Earth causes Destruction of Property--
Causal links between an action and a destructive outcome are only valid if you are directly causing a destructive outcome, in an invasive way. Trespass, not mere withholding of resources in transit.
For example, polluting a river next to a village is argued to be aggression because you're sending pollutants into the village without their consent.

With trying to stop sunlight from reaching Earth, only messing with sunlight before it's reached Earth, you aren't aggressing because no foreign matter trespasses property borders, there is no invasion. This is a mere withholding of a Natural Input.
This does not constitute invasion, same as slowly draining a large unowned body of water. If others like using it from time to time but nobody claims ownership, you can't argue aggression. Nobody is entitled to an unowned body of water. The same applies to the sun.

Imagine Alice likes going to an unowned forest once a week and eating berries from it. Now imagine Gerald homesteads and cuts down the forest. Now Alice can no longer get her berries. Aggression? No.
Now imagine Alice also used the berries she collected to power a machine that made her garden grow, and without the berries her factory will stop functioning and her garden will die.
Does this suddenly make it aggression since now her property's integrity is linked to the berries? Of course not. She has no entitlement to the berries.
 

--Entitlement through a Right to Easement, a Pattern of Use--
Perhaps humans own the sunlight and have a right to easement of the sun, they don't own the sun but they have partial homesteading of the sun due to continuous use of the sunlight from it.

By this logic, the hobo's continuous, visible harvesting of fallen berries constitutes homesteading of the recurring yield itself as a pattern of use. Not the bushes themselves, but the recurring yield.
This is a very vague assertion though, and feels kind of like Squatter's Rights being implicitly snuck in, continuous use of a house doesn't necessitate a right over the house in and of itself, right?

Imagine Alice again, she likes going to an unowned forest once a week and eating berries from it. Gerald homesteads and cuts down the forest. Is this aggression or not? Surely not, yet Alice has a pattern of use in connection to the forest, therefore Squatter's Rig- I mean uh,  a right to the continued pattern of use of the forest?
 

--But the Natural State of Humanity is to have access to Sunlight--
Imagine a hobo who lives on an island. The hobo builds a house, the house is his property as he homesteaded it. He lives off of berries from berry bushes, but he never interacts with the bushes, he merely picks up berries off the ground that fall off the bushes.

The berry bushes should thus be unowned, dependency does not create entitlement. If Johnny comes to the island and starts homesteading and uprooting the bushes, this should not qualify as aggression because the bushes are unowned and the hobo has no entitlement to them.

1. Hobo relies on berries fallen off bush
2. Humanity relies on sunlight from sun randomly reaching their planet
There is no valid difference here. The only difference is that humans are born into relying on the sun, the "natural conditions". This doesn't hold up because you can argue the hobo has the natural condition of having access to the berries, as he was born on the island. What defines natural?
Dependency should not grant entitlement, that contradicts the NAP.