This is pretty much Proudhon in a nutshell.
But the easiest way to understand how original appropriation cannot be justified within a conservative/libertarian framework is by focusing on the idea of opportunity costs. When an individual declares perpetual ownership of some piece of unowned land, every other human being on earth suffers an opportunity cost: their opportunity to use that land has now disappeared. Opportunity costs are real economic harms.
To be concrete about this, consider an example. The piece of land down by the river is owned by no one; so everyone can use it. Sarah declares — on whatever property theory she prefers — that the piece of land by the river now belongs to her exclusively. But, wait a minute. The previous ability of others to use the land by the river has now vanished! They have been hit with opportunity costs. If one of the dispossessed were to say “this is silly, I do not consent to giving up my pre-existing opportunity to use the land down by the river,” Sarah uses violence (typically state violence) to keep the dispossessed out.
Unless unanimous consent exists, the original grabbing up of property results in violent, non-consensual theft from others. It is really just that simple. What follows from that conclusion is that the conservative/libertarian positions that depend on the sanctity of property rights are totally bogus. For instance, you cannot complain that taxes violently take material resources from you without your consent when property itself is predicated on just that. You cannot claim your enormous wealth was gotten fairly when the ownership of that wealth is predicated upon the non-consensual violence just discussed.
This basically skewers the “homesteading principle” which is at the core of most, if not all, right-libertarian property rights. The only thing (I am aware of) that tried to tackle this, is the Lockean proviso, which has its own, very significant failings in regard to the loss of freedom from such enclosed lands.