Student contribution/Citizen science?
A link to Academia is your best bet.

Stay in touch with people doing research in the field of your interest in a formal setting.
If you come up with a notable work you may end up co-publishing it with them.

Open source is a great alternative

There are many, many notable pieces of code developed (and credited to) individuals no tied to major organizations to be found i.e. on GitHub. This is a good way to quickly put your results thru "peer review", albeit informally, get credit for your work and -why not- good PR.