How likely is it for an 8cm ovarian cyst to go away on it's own in the first trimester of pregnancy?

Unlikely: Its unlikely that it will go away, but it's also unlikely that it will cause a problem. The most concerning risks are torsion or rupture. Cancer is also a risk but very unlikely. Typically these cysts are followed intermittently with ultrasound during pregnancy. If you end up with a c/s, your doctor can look at it then and take it out.