Let's say that I want to learn more about the Roman Empire, the politics, the public opinion about it but i dont want to rely directly to books or academic, how i am supposed to search for sources of this time period? I know i could go to the academic paper/book sources but the choices of those sources could be biased towards the author's opinion, so How do i search for this type of information?
First, we should just make it clear that you probably can't successfully interpret or use primary sources without more training. It's not a simple thing of just looking it up and saying, "oh, I get how this scrap of paper contributes to a broader historical argument."
But let's say that you're really willing to put in the time to learn how to do history and you're just trying to figure out how to go about it. If you were an undergraduate I'd point you to a reference librarian who can tell about local or e-resources — the kinds of things that are relatively "accessible." But if you were a serious scholar, I'd give you advice something like the following:
First, you do want to do a literature review and see what kinds of sources other scholars have used. Usually you'll find that most sources cluster in a few places, depending on the field and subject. For example, if you looked at my sources you'd find that a lot of them were kept in the National Archives and Records Administration, College Park, facility. Great. Now you go to that facility, and you talk to the archivists there about how their file organization works. Then you could consult the sources I consulted (to see if I used them right, if you want), and you can also look at the other sources that might be at the same facility. Repeat for all of the facilities/files you are interested in.
Beyond that — finding "new" or "unused" sources is difficult. They usually don't just advertise themselves in an obvious way, or else someone would have looked at them already. But when you get steeped in a field and have very specific research questions you are trying to answer, you tend to find ways to ferret out likely locations for sources. Sometimes this happens through word of mouth (someone says, "oh, I heard XYZ has some un-catalogued material on that subject"), sometimes it happens by sending e-mails or calling places that might have records, sometimes it is just happenstance.
But to get at the main point again: rarely do you forge "new" ground in finding sources. You start with the ones that are already out there. It doesn't really matter if other people "chose" them based on their own "biases": it tells you where they are. Then you go to them and apply your own interpretive framework. None of this is quick. It takes half a decade to write a PhD thesis. I can take well over a decade to get deep into a field of research to the point where you can find new sources, make novel and plausible interpretations, and so on. History is a form of expertise, and you have to put in the time if you are going to really contribute.