Yes, it is possible, a bit of common sense needs to be applied with a bit of knowledge on how to figure out where the gold might have originally came from.
Start with some common, very simple, things.
1) Gravity sucks. Everything goes downhill. So of course look upstream/uphill.
2) Look at the gold you are getting under a loupe or microscope. Why? Gold is a soft metal and gets worn easy as it bumps and grinds along downstream. Quickly it becomes rounded, and you can see under a microscope other particles like sand imbeded in it, as well as a coating of elemental carbon from the environment. You may also have multiple sources of gold upstream. So some gold may be fresh and shiny and very well defined with crisp lines that it got from the host rock. This is most likely then from a nearby source. If it is well-worn gold it might be far upriver or upstream OR it could come from a nearby auriferous gravel deposit that has lain buried a long long time and is now getting eroded and dumped back into the river, so ...
3) Look around for ancient deposits of river gravels. Although the world looks how it does today, the gold you found may have travelled down a river millions of years ago, was caught in a pocket with other gold, then buried and eventually over time, with erosion, that layer of rocks and gold may have become exposed and is now 'leaking' into the stream or river that you are now finding it in.
4) Sometimes a stream may be cutting through a vein of rock that has a seam of gold in it. And it may be on the bottom of the river or stream. As other rocks tumble along and break chunks of it off, it releases some of the gold into the stream. Look for seams of quartz or other minerals commonly associated with gold that may be crossing the streambed.
5) Sample sample sample. If you found some very shiny new gold, for example, sample the river or streambed every 100 feet or so or where it is practical, looking for small flakes that are like the ones you already found. If suddenly you run out of them, it's most likely that you are now just past the source. Backtrack and test frequently and find where you pick it up again then look up the banks on either side of the river (and the bottom if you can) and see if you can locate the source. Take samples from the bank or hillside and test them.
All in all it might be tedious work, depending where you are, but it can be very rewarding. You could strike it rich! If I were at the mouth of the Columbia river and found a gold flake I doubt that I would attempt tracking it down. If I were at a branch in a small creek that drains a small basin, the source of which is just a mile or two away, I would bust my ass tryin to find it because I know that it can't have travelled far.
So that's basically how the old timers did it a long time ago. Another method they used was getting up very early and following a successful miner out to his claim then grabbed the claim next to him!
Well I am not the worlds foremost expert on this stuff, but I do hope that it helps you some. I am sure there are others in this forum that can add to what I have said, and perhaps give you additional tips, or who knows, correct me where I err...