Voting can have an effect, of course, but whether it does is dependent on many things.
if it were true that voting does nothing, nobody would put such effort into discouraging us from voting
This is not necessarily correct.
Never assume that the thing that an opponent loudly and visibly opposes is their actual goal; it may very well be a distraction to keep you from their real goal/ or the real threat to them. That's not some abstract hypothetical, either; this is done all the time in politics. Putting non-starter provisions in bills in order to expend your opponents' political capital killing the extreme provisions in order to get your real goals passed, is a common practice, as one example.
An inexperienced opponent telegraphs their real moves unwittingly. An experienced one feints.