I think I Like to Code's answer is spot on, and I would like to reinforce that it is a strenuous path and potentially frustrating goal to perform research independently without any formal training on how to do so.
I would like to add, however, that a realizable path is to attempt to do (voluntary) work in another institution for some period of time. That could be done, for instance, during your vacation time (summer/winter). If your institution is unknown and you have nobody to vouch for you, it may be difficult to convince a professor to take you even for a short period of time during the summer, but that's far less unheard of than becoming a successful lone researcher. We've had several undergraduate students from local colleges work with us during short periods of time. Many ended up being co-authors in papers we published and/or were successful in securing a good Master/PhD.
Better yet would be to organize with your current institution to spend part of your studies in a research-intensive institution (3-6+ months). Even if that's not explicitly encouraged or allowed, there's always the possibility of you trying to convince them that this would be something you desire and believe would be useful to your career in the future. You can also try to convince them to give you credits for that (replacing elective courses or something like that).
If you can secure a formal research position, even if only for a short period of time, it's much more likely that you will be able to continue working from home, potentially following up on what you started on the formal position, especially if your research involves only pen/paper/computer.
As a data point, I did exactly that during my undergraduate. Even though my undergraduate institution is relatively well-known and research intensive, I went to the US as an exchange student and worked with a famous professor for a short period of time. Upon returning to my home country, I joined another professor's lab but continued to work remotely with the US group. I ended up publishing two papers as first author with the US group in very good journals before I even finished my undergraduate, and presented my work in an international conference.