Can I set the cohort to share with everyone by default?

Hi Mana! Julianne from Mixpanel Support here. I hate to be the bearer of bad news, but it isn't possible to change the default cohort settings at this time. Sorry I don't have better news there! I definitely recommend submitting your use case and request for this feature via the 'Submit Feedback' form (under the ? menu). This will flag your use case and support of the feature to the Product team. They use the logged gaps to develop future releases and improvements of the product.