I don't disagree with the other answers, but here's a different perspective you should bear in mind. Also, I can offer answers to your specific questions as someone who left academia (applied math/CS) for data science.
In short, understanding the underlying needs and use cases for a business problem is paramount to any project, and so developing a strong business sense and cross-functional communication skills are critical if you want the broadest reach in a data science career.
* Can I still get hired at this point (I mean, after finishing this semester with the knowledge described above)? I honestly think I am not ready, but I feel confident that I can get decent in a year.
* Am I being too naive in thinking a company would give me a chance?
I'm going to answer these together. It strongly depends on the company and its current needs. For you, this might vary along the dimensions "startup" to "enterprise" and "ML shop" to "general data-driven business". By the latter, I mean there are companies whose sole purpose is to sell ML products or services to clients, vs. 57
general tech companies that want to exploit modeling in their business. Chances are you'll find a quicker/easier fit with a company that either already has its ML use cases built out or dictated by others, because you're not likely to be equipped to strategize the inception of a new project.
So, that could be true of a larger business that has a department dedicated to grinding away on ML model technicalities while other parts of the company determine business strategy and design, or in a business of any size that is focused on ML as its product/service.
In the short term, yes you can probably convince someone to have you as an intern or assistant on some projects, but your PhD will likely be seen as a potential drawback if you're talking to small to medium companies who want to hire generalists/jacks of all trades...
* What should I do to become more hirable in any case?
Which brings me to this. You can choose your own adventure because there are so many types of role, but you should be aware of what kind of role and situation each potential employer is looking for, and be realistic about how you might fit with it. There are lots of employers who don't clearly express what they want or need, or don't even know themselves what that is. You'd do well to figure that out with them to avoid heavy disappointment.
If you want to broaden your horizons in data science and ensure you have the highest business impact and professional development opportunities, you'd want to learn a lot more about business applications of data science. Those are highly diverse and both more informal in practice and more impactful to the business overall than worrying about optimizations for pseudo-inverting matrices.
Despite the reasonable opinions in the other posted answers about the market, there's a huge market deficit in my opinion for data scientists who:
* Truly understand business needs and can communicate effectively with non-technical people
* Develop and execute plans that involve general data-driven problem solving, which may or may not involve building "cool" models (and frankly they probably won't, at least not until the problem is very well understood by more traditional exploratory methods). 57