Simply there is no way to do that with JavaScript because the “default search/homepage” is a user’s preference and you do not have access to that without user’s permission because that would be a security/privacy issue.
What Google does at every user visit is show a promo ad with a close icon and a go button with instructions on how to set it as the default homepage. On click of any one of them, it creates 2 cookies so that next time it will check your cookies and make the promos disappear. Even when Google is your homepage and you clear your cookies then a banner is still there to promote Google as your homepage.
I have checked this with Firefox, not aware of Chrome.