I have this:
but I want the rest in the beginning of the measure. How do I do that?
Unfortunately, there's currently no option in MuseScore to move notes horizontally, nor is there anything akin to an "insert" mode.
As such, the best solution here will be a simple cut-and-paste work around. Select all of the pitches you want to keep, copy them, and paste them (in this case) starting on the second eighth note of the measure. Then, replace the opening of the measure with an eighth rest.
See also https://musescore.org/en/node/11944, a discussion which reaches the same conclusion.
If this feature is really necessary for you, there are two things you might consider:
c8 e g r) but you want to put the rest first, all you have to do is move it:
r8 c e g.