This is probably only useful for people who want to tell a story with a specific premise but maybe someone wants their early galaxy to look a specific way. There is a way to do this via DB editing which is probably faster but leaves you open to issues, since DB editing is inherently risky. So, if you would rather not do that, here's how to do things through in-game options thanks to SM mode.
We will create a game setup where Sol only has 1 JP that connects to Proxima Centauri, which in turn has only 2 JPs, one to Sol and the other to Alpha Centauri. First, create a new game with the settings you want. Then create the player race but don't make it your actual player race - this SM-race is only used to create the setup of systems and will be deleted later. Turn SM mode on and go to the System Generation and Display Window. Click "Full Grav Survey" on the bottom left corner. This will reveal how many JPs there are in Sol. Use the "Del Jump Point" button until there is only one JP left. Select it and then click "Explore JP". This will create a new system and move you to it.
Odds are, this new system is not Proxima Centauri. That's okay, find the "Delete System" button on the right edge of the bottom row of buttons and click it. Double confirm windows and you'll be back in Sol and the JP should have gone back to showing "Unexplored". So, you can immediately click "Explore JP" again. If it's not the system you want, then rinse & repeat, until you get Proxima Centauri. Once that is done, click "Full Grav Survey" while you're in the Proxima Centauri window and delete the extra jump points until you have 1 leading to Sol and 1 unexplored. Now you can repeat the previous process until you get Alpha Centauri.
Deleting systems this way is harmless as they can be re-discovered, they are not deleted from the game, just from the knowledge of this race. You can also edit the systems if they too many bodies or not enough bodies. For example, for my campaign I want Alpha Centauri to be loaded with good real estate so I will adjust the planets a bit. The final step is to go back to Sol, create a new player race on Earth and then deleting the SM-race you used before. This way, you can start your campaign with a race that has absolutely no knowledge of the process you just went through, to minimise the risk of any problems down the line, especially important since currently the "No Grav Survey" button does not work, meaning that if you do this process with your actual player race, there is no way to remove the knowledge of these systems and JPs. Now you can play the game normally, survey and explore and so on.
