Can I submit a review paper to a journal without being invited?
Yes, it is absolutely possible to write a review paper without being invited to do so.

How do I know this?

I've done it, several times, in the biological sciences.

The key is to recognize that the review needs to be invited at some point, but that point need not be "before you've written anything down*. If you have a target journal, and you think it is a decent fit for the review paper, I would suggest that you find the email for the appropriate section editor (or the Editor-in-Chief if there is none) and write them a polite email inquiring as to whether or not they would be interested in inviting a review on X topic, a draft of which is attached. Articulate why you think this is useful and interesting to their readership, and hope for the best.

And before we get on the "A PhD isn't enough clout to write a review", my first review was published with an undergraduate as the primary author.