I think we should start with the low-hanging fruit: most governments control large areas of land that are not yet designated as nature reserves but could be. They're currently used for logging, grazing, mining, etc. Simply switch the classification and we'd gain a huge amount of nature reserve without needing to oust or even regulate a single private owner. Ditto oceans, there's a lot in national control that could be switched over.
We could also employ a bunch of people as conservationists just by letting rural folks sign up for a program that would pay them to keep their land in a natural state. This would make it feasible for people to repopulate a lot of areas that are losing population, thus reducing the flow into already overcrowded cities. Mine is a bit catch-as-catch-can but it sure has more wildlife than surrounding farms. Imagine what someone could do with a few dozen or hundred acres in Vermont. This would also let us convert marginal cropland to healthy shortgrass prairie, without running farmers out of house and home. Here, we'll pay you to quit trying to grow wheat and grow native grasses instead.