timerover51... Good, You should not have any problems accomplishing it.
You know that there are "things" to get around but it can be accomplished.
If you use a so called Nature CIV, it is best to have it only for the AI and set at constant War with all others and no contact possible.
Use that and also have Nature be able to build Wonders that place Improvements in ALL of its buildings...even Two Improvements. Then use your resources to "activate" those Improvements to start Auto-producing Units when you want.
You can still have Nature Directly Be able to build other Units as you desire.
The Human Player cannot play as Nature or even make Peace so this helps the Game Play as one would want.
Simply set Nature to be able to build Wonders (by any other Name) and set those "Wonders" to place Improvements that will Auto-Produce Units for Nature. The Wonders can also Auto-Produce Units from the Start..... but the Improvements will Not start Auto-Producing Units until the Resources are gained.
In Other words... when a Wonder places any Improvement that Requires a Resource to be able to build that Improvement, the Benefits are there as Flagged when placed, But the Auto-Production of the units cannot start until the Resources are obtained.
We all know that the AI does Not tend to build Wonders or Improvements when at war as much as it does Units.... so at the start of the Game, the AI has the chance to build Wonders and especially if the Wonders do not cost so much that many turns are needed and also if the Wonders provide Great benefits.
So simply take advantage of this and have the AI build any number of Wonders from the Start and have those Wonders place Improvements that require a Particular Resource to be built. Also have those Improvements Auto-Produce a Unit.
You can then dictate when you want the Improvement to start Auto-producing the unit by dictating when the Resource is gained.
The thing is, ALL of the cities that have the Improvement will produce the Unit exactly at the same time because the Improvement was placed at the same time by the Wonder.
Thought will tell you that, for example, if you set an Improvement to Auto-Produce a Unit every 12 turns and the Improvement is placed by a Wonder. IF the Resource that is required to build the Improvement is obtained 12 or more turns after the Wonder places the Improvement, ALL Cities will instantly have the Unit when the Resource is Obtained = Hordes.
You can use this to make Hordes of units that the AI will use at that time.... then after that, the Improvement will continue to produce at the rate you set and or go Obsolete as you set up.
Personally, I like to have games at least have what I have called "Plausible Reality" or in other words, have it seem possible in some remote way, at least in the game
Unless you have all CIVs only have 1 ERA, you will have problems with Nature having a 1 ERA Tech Tree because all require the same to advance to the next ERA..... So Set Nature with 1 ERA and adjust the Costs of the Techs for that so Nature will require more turns to get through the Their Tech Tree. You can also set Units to require No Support for Nature so Nature can handle many units and continue through its Tech Tree. This will require experimenting and Testing to get the Balance You want.
On an Off Note... you can use Upgrades of a single Unit that can be captured by all CIVs, including Nature, that can Upgrade to different units for each CIV. Many ways to go about adding Animals or even a separate CIV as Nature to accomplish what you want.
I believe you can accomplish adding Dinosaurs or anything you like to have the Game you want.
As has been said many times here... "Think Out of the Box" ... you will succeed.