You cannot send a probe to the Moon or Mars until you have completed the specific "Mission to [Planet]" research project. Once researched, select the planet and use the launch button at the bottom center of the screen.
Hire at least two councilors with high Persuasion scores. Your immediate goal is to win over small nations quickly to build influence before tackling global powers. Terra.Invicta.v0.3.35.Early.Access.zip
Build MC in every nation you control. You will need a significant amount of it to maintain your initial space stations and mining bases. You cannot send a probe to the Moon
Use the feature added in 0.3.35 to hide outdated ship components and finished projects, making it easier to manage the massive tech tree. Your immediate goal is to win over small
Assign two councilors to "Control Nation" missions in countries with high success chances. Use your third councilor to "Investigate Alien Activity" to begin uncovering the alien plot.