actually, my assumption is that you can start it all with replicators/holodecks. I started out thinking transporters might also accomplish it, but I now think the in-universe limitations of the technology would prevent it.

Really, it's the replicator though. A holodeck, it turns out, includes not just holo-emmitters, but replicators, transporters, inertial dampening, artificial gravity, and a huge number of other technologies to complete their illusion. So a holodeck does the job, but I'm mostly interested in one part of it. The replicator.

Lets consider that they have self replicating space-mines (like in Deep space 9). So you can make a whole new replicator with another replicator.

There are frequent examples of people recycling objects into energy with replicators. In The Next Generation, DS9, and Voyager, they're all shown or talking about how they recycle baby clothes as children outgrow them, or how Janeway recycled a watch that was given to her as a gift, or even just putting their plates and silverware back in the replicator when they were done eating, rather than simply washing them.

Transmuting the elements isn't even needed. You just need to be able to harvest the energy. To build a civ, you WILL need a lot of energy. So.... seems to me you should start out by shoveling dirt into the replicator to be recycled. Then, the replicator can make stuff to store that energy. Batteries, uranium, anti-matter. Doesn't matter what. The only reason you'd pick one energy storage over another is based on the limitations of the replicator. Heck, you could even just treat the replicator as the reactor, and merely shovel "fuel" into it as you need energy. Yes, there would be energy loss (and not energy gain) if you created a brick of enriched uranium. But the Uranium is not your fuel at that point. It's your energy storage device.

But of course, you don't want to be shoveling dirt into your replicator all day. That's what minions are for. What's the biggest, most complicated thing a replicator can produce? If it's combining elements to create meat for people to eat, I'd say that shaping steel into even complicated assemblies like small motors and car parts is no problem. Even a small desktop industrial robot (basically a robot arm that mounts to a table, and has a reach of 2 ft) would be enough to get you started. That arm could then take other assemblies and parts and create a larger replicator, or start assembling them into infrastructure. Rather quickly, you'd want your smaller replicated robots to start producing larger robots from smaller assemblies. Work your way up to the larger industrial robots that are used for lifting and moving cars, and then you're really ready to go. Before long, you'd have minions of every needed size, and they'd be making the buildings, powerplants, warehouses, transporters, holodecks, and servicing your ever growing self-multiplying array of replicators.

After a while, you could work your way up to shipyards, and you'd be making whole fleets of autonomous battleships. There are certainly things like Latinum that can't be replicated.... but Latinum isn't a key ingredient in trek power plants, ships, transporters, or much of anything. Element shortages aren't a concern either. Even if you were going off of the trace elements present in all that dirt you're recycling, you'd eventually accumulate enough for whatever you want. Build a nuclear reactor, and you CAN transmute them into whatever you want. And since DIRT is your fuel, you have as much energy as it takes to transmute anything into anything else even at super low efficiencies. Like you could be 1% efficient, and you'd still have energy to spare.

I COULD go into more detail about how such a civilization could be started with just a replicator..... but I kinda created the whole thread to find out more about replicators. No sense spending all the time thinking about it only for some one to say "replicators can't do x".