There are many assumptions bundled up in your question which I think need to be addressed.
Firstly, a bachelor's thesis and a research paper in physics are very different, in almost every aspect (content, length, aim, purpose, style etc). It is perfectly possible to write a bachelor's thesis on a topic and then rewrite part of it as a paper that you then submit to a journal for peer review and publication, and it is also possible to incorporate the findings of a published paper in a bachelor's thesis. However, I do not know of any journal (in physics at least) that would simply publish a bachelor's thesis as it is.
Secondly, it is extremely rare for a bachelor's thesis to contain actual novel research. In some countries, it's rare for a Master's thesis to contain novel research. The main purpose of a bachelor's thesis is to give the student a chance to develop their literature review and writing skills. Typically you would write about the history of a certain topic in physics, and perhaps discuss some recent findings or developments. In my bachelor's thesis, I wrote about Noether's theorem, describing its history, showing a couple of basic proofs and talking about how the theorem can be applied to orbital mechanics. Obviously I am not Emmy Noether; none of this was my own original research.
Thirdly, I expect you will find it extremely difficult to progress without supervision. You mentioned that you have contacted various professors. Are they all at your university? Have you tried contacting professors at other universities to see if they would supervise you remotely? And have you considered contacting PhD students or postdocs instead of professors? They may have more time to devote to you and could possibly provide more hands-on supervision.
If you do write a thesis but your university does not offer it as an official part of your degree (i.e. it will not appear on your transcript in any way), then the best "proof" that I can think of would be to show the finished thesis to whichever of your professors you are closest to (do you have a personal tutor or equivalent?) and ask them to mention it when they write reference letters for you. That way you have their word as well as your own that it is your work.
Alternatively you could consider posting it on your own website, or putting it on arXiv as a preprint. I would think carefully about the latter option, however, as you cannot delete things from arXiv and, as your personal standards improve and you move on to more in-depth research, you may not want your bachelor's thesis to remain public five, ten or twenty years down the line.
Edited to address the new details provided:
It sounds like you have some ideas for a research paper and you want to publish it when you have finished it. Your professor told you that it's better to publish your paper in a journal rather than on arXiv, which is true. ArXiv is a preprint server and does not provide peer review, unlike a journal.
Submitting your paper for publication is fairly easy. Firstly you need to identify an appropriate journal for your submission. I'd suggest asking your professor for advice on this, but it sounds like they are not the most helpful. A good way to decide on a journal is to look at the papers you cite in your paper and the journals those are published in.
Be aware that journals have different standards for submission and for some journals, it is common to receive a "desk rejection" i.e. your paper is rejected by the editor before going out for peer review, either because the editor thinks your paper does not fit within the topic of that journal, or because it is insufficiently novel or otherwise of low quality.
Once you have identified a suitable journal, navigate to the website of that journal. There will be an obvious link to click called "submit" or something similar. Click that link and follow the instructions given. Then, if you do not receive a desk rejection, you will have to wait (perhaps a month or two) to get the referee report. You may have to make corrections or alterations to your paper based on the referee report. If you do that satisfactorily, your paper will be accepted and published in the journal.
In physics, it is typical to upload a copy of your paper to arXiv. In my subfield, it's common to post to arXiv, wait a couple of days for the inevitable "you didn't cite me" emails, then submit to the journal. Once the paper has been published, you can then update the version on arXiv. You can check the arXiv help page for information on how to get endorsed: https://arxiv.org/help/endorsement.