This happens sometimes, but I don't think it's endemic. I've seen people come in a day late, even in questions where an answer has been accepted, and get tons of votes. It just has to be obviously much better than the others and you have to hope the stars don't align against you (as with so many things in life). The "fastest gun" problem typically occurs when the best answer does not really stand out to people.
For example, glancing at my top five answers, one of them was posted the day after the others in the question and got four times as many votes as the next top answer. I remember that at the time I wrote my answer, a very low-quality answer from somebody who didn't know Ruby very well was accepted, but now mine is accepted and the other guy graciously deleted his.
And that one's still getting votes. People come across those old questions and vote the good answers up years later. So the site can correct itself as long as people are willing to do that.
Unless something has changed, you need a minimum level of reputation to upvote. If you are not a member of the site (I have a vague memory of starting with only 10 rep - I have no idea now) you have no mechanism to actually do as you suggest until after you've posted or asked a question that has gotten at least one vote.
I just created an account there after years of lurking and absorbing knowledge from other's questions and answers, but I only have 1 rep.
Oddly enough, I created the account specifically to upvote the answer that solved my problem of which another member had asked about, but I am unable to do so until I submit a problem of my own that has not already been answered.
Yeah, that's still true — people who haven't participated in the site cannot upvote. I'm not sure if there was a larger point that I'm missing. Things still get upvoted quite a bit even with the rep requirement (and you could make a reasonable argument that the rep requirement means the votes you get are marginally better indicators of quality).
For example, glancing at my top five answers, one of them was posted the day after the others in the question and got four times as many votes as the next top answer. I remember that at the time I wrote my answer, a very low-quality answer from somebody who didn't know Ruby very well was accepted, but now mine is accepted and the other guy graciously deleted his.
And that one's still getting votes. People come across those old questions and vote the good answers up years later. So the site can correct itself as long as people are willing to do that.