My immediate, knee-jerk reaction is:
"Ha! Obviously the Holodeck! This is easy!"
However, then I comprehend the uses of the transporter...
I don't understand why there is still a debate - I thought I won the thread.
Step 1: Bring some bulk raw materials into your holodeck from the outside world.
Step 2. Have the holodeck generate a machine or machines that can take those raw materials and process them into equipment.
Step 3. Have the machine make these items in this order:
1. 24th century power generation system of some kind - ask the holodeck computer what is appropriate - suitable to run a shuttlecraft. Probably a small warp or anti-matter reactor.
2. A shuttle shield generator. As soon as this is complete, set up the shield generator and the reactor outside the holodeck to defend it with.
3. A hand phaser. Power it up from the reactor, then use it to defend the holodeck and reactor. Probably unnecessary with the shield, but let's not tempt it.
4. A small launch vehicle, a small mobile satellite armed with shield and a phaser, sensors, and a handheld control unit. Send those up to better defend the whole setup and provide sensor data for the next step.
5. Now you make your transporter. It can be a single platform, and this can use up the last of the raw materials you brought in, because from this point forward, you can beam in any additional material needed.
I'm going to stop here, because I think it is pretty obvious how to continue at this point to get to having your own starship in orbit, as well as to conquering Earth.