When client calls you next day of his website launching public to complain about his site not showing on Google results.

Face palm

always tell your customer that it takes a while for Google to index the site. And also tell you're not Google haha

That happened ten years ago. What I allways tell them is that only those who he gives the link will acces the website unless they do constant work on analytics and content/SEO and wait...

My boss once told a client that she would talk with Google and arrange a good position :/

Yeah sure. you have to "tell" Google your website exist.

Well that was not the smartest boss, right?

It is a complex question, It can't be said she wasn't smart, she built a quite big business , had her skills, but in some fields she was absolutly dumb, computers was one of this fields.