Not very likely. The BLM, or rather the various agencies it is descended from, go back to before the Constitution.
The federal government has held title to this land since it was acquired by the USA via the Treaty of Guadelupe Hidalgo in 1848.
Unless the gentleman can provide some documentation of his title to it. We don't generally allow people to take over a few hundred thousand acres of land simply by claiming ownership.
The BLM was created in 1946. His family goes back at least three generations on that property.
>> “ The BLM, or rather the various agencies it is descended from, go back to before the Constitution” <<
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That is gibberish!
Do you have the slightest idea when the US gained title to Nevada, and the conditions under which it did so?
All private land claims take precedence in these purchases, so the BLM or it’s predecessor have the weakest of all claims to any particular parcel.