No you cannot. TN requires you to have specialized degree. You can only be sponsored for H1-B by an employer (hired and move same time).
When I interviewed with Google and Facebook a few years ago, neither of them were concerned that I don't have a bachelor's degree (I have a 2 year post-secondary diploma). I can't remember which one it was, but one of them thought they'd be able to get me an O-1 visa as a backup plan if a TN was unexpectedly rejected.