In short, other independent and contemporary sources overwhelmingly point to Socrates being a real person, and not just a figment of Plato's imagination.

The assumption that the historicity of Socrates isn't questioned, while the historicity of Jesus is heavily debated, is inaccurate. The questions of the historicity of both Socrates and Jesus are questions that have been asked many times in history and a lot has been written on the subject. Both these subjects even have their dedicated wikipedia pages, if that counts for anything. Of course, these questions (more so the question about Jesus than about Socrates), have an ideological side to it. As always, when reading texts on this subject, it is good to keep the general historically critical viewpoint in mind (i.e. who wrote this, who published this, could they have ulterior motives to do so, what are the possible biases of the authors, etc.)

Let's get Jesus out of the way first. It seems to me that the idea of Jesus as a completely fictional character created by the early christian church is not as widespread as you might think. Although non-biblical sources on Jesus are rare, there are a few which are seen as reliable, most notably the writings of historians Flavius Josephus and Tacitus. I'm not aware of a poll that states what percentage of current historians agree on the existence of historical Jesus, but I've never (excuse my anecdotal evidence) actually talked to a historian or philosopher who made the explicit claim that Jesus is just a fictional character.

Now on to Socrates. The most glaring evidence of the historical existence of Socrates is that Plato's dialogues are not the only sources mentioning Socrates. Other contemporary sources exist. Most famously, Xenophon also writes about Socrates (four of his works are about or mention Socrates).

Another source mentioning Socrates is The Clouds by Athenian playwright Aristophanes. This work satirises Socrates and philosophers in general, contrary to Plato and Xenophon who treat Socrates with the greatest respect.

Other followers of Socrates who wrote about him are Aeschines and Antisthenes. Their writings are unfortunately lost, but ancient authors who still had (partial) access to them mention them. Aeschines is thought to have wrote seven Socratic dialogues, and Antisthenes works supposed to have filled ten volumes, of course not all being about Socrates. Both these claims are made by Diogenes Laertius in his compendium of ancient philosophers.

So to summarise, it is safe to say that Socrates was a real historical person. He is mentioned by several sources independent of Plato. And he is even mentioned somewhat negatively by Aristophanes, who was not a philosopher or follower of Socrates.