Approaching unresponsive high level research professor as an undergraduate without any program

Well, faculty-student research is a two-way street, and for whatever reason, it certainly doesn't sound like this professor is showing a lot of interest in working with you. This is not necessarily anything about you or your abilities; he may just be busy with other things, or not very interested in working with undergraduates in general, or too disorganized to keep track of potential research students. But any of those would suggest that this is not someone that would be a good research supervisor for you at this time.

If you did start a research project with this professor, you'd be counting on him for actual supervision: advice on what to learn and what to work on, feedback on your progress and on your products (papers, code, etc), availability to meet to help get you unstuck when you are stuck on a problem, signing necessary university paperwork, collaboration in writing and submitting papers if you get that far, and so on. You can see from many questions on this site how frustrating a research experience can be if this sort of support is not forthcoming, and it will be especially important in your case since it's apparently your first time getting involved in research. And the fact that he is already so unresponsive to something as simple as "I'd like to talk about research opportunities" is reason for serious concern that he'd be similarly unresponsive when you really need his participation.

I would suggest that, at least for now, you move on and look for research opportunities with other faculty members - ideally, someone with a record of working successfully with undergraduates, and who shows clear interest in working with you. I think these are more important than a perfect fit of research interests.

You have plenty of time to consider approaching this professor again in a year or two. In the meantime, you might try to talk to other students he's supervised (either undergraduate or graduate) and find out how the experience was. This may give you some ideas about how to get his attention more effectively, or it may convince you that you don't want to work with him at all.

One option is to take a class he teaches and do a fantastic job there, especially if it is a graduate-level one. Those classes often involve projects that deal with the actual research in the field. Very often those projects are open-ended and can potentially result in publications. I even suspect that some professors deliberately use their class projects to look for new students. If you can make yourself stand out from the crowd there, it is likely to open some doors for you. But since you are a freshman, make sure you are actually well-prepared to shine in such class before enrolling. Sometimes it is better to be patient and prepare well.

Another thing is to not get fixated on a particular sub-field. Research interests evolve over time, especially at an early stage. It is likely that in a couple of years you will be super hyped about doing something else. So enjoy your time at the university, learn as much as you can, and be open-minded about what you can do with your knowledge and intellectual abilities!

I'll just guess that he doesn't think you are ready and that he doesn't have the patience to deal with you at your current state of development. But, just a guess, as I said. You might have better luck in a year when you have a few more courses under your belt and some "seasoning". If you close the intellectual distance a bit you might have a better chance.

But another option, that might work, is to work through a different professor who has a high opinion of you and might be willing to get you connected to the "big guy". A recommendation from a colleague holds some weight where an email does not.