I searched online and came across people who think he almost certainly existed, and others who are skeptical.
Early Rome is a hugely tricky area of history (and a relatively unpopular one in English-speaking circles), precisely because the evidence is so sparse and the majority of the evidence is the literary tradition (mainly Livy) that was created hundreds of years later, though using older documents and inscriptions, particularly the consular fasti. As such, without a grave that says "Tarquin the Proud" on it (in the Etruscan language that we understand so poorly, presumably), you will always have people that dispute the literary tradition.
However, throwing out the tradition of the Tarquins completely is fairly overzealous. In my mind, that would be sort of a 'throwing the baby out with the bathwater' scenario. They are not like Romulus, the story of whom shares similarities with countless mythical and semi-mythical heroes in various cultures (abandoned as a child/born out of wedlock, raised by animals, killed somebody, led a people, etc). While we may doubt many of the details of the Tarquinian narrative, there is nothing really unbelievable about their very existence or their Etruscan origin. Early Rome had a significant Etruscan population, and it was not unusual in that part of Italy in general for great families to move around and assume positions of power elsewhere. There is evidence of important Latins in Etruscan cities, and of course much evidence of Etruscans in Rome. Likewise, there is no reason to doubt that the Tarquins were overthrown violently. The late sixth century and early fifth century was a time of great upheaval all throughout Italy, and while the details of this are poorly understood, there was clearly a lot of political violence. We have evidence of this from archaeological finds telling us there was a fair bit of destruction in Rome and numerous other major cities around this time.
It is entirely possible that the Tarquins, Superbus in particular, have had their role exaggerated. For instance, one poorly understood figure but clearly pivotal figure, Lars Porsenna, who was Superbus' first big ally after the latter was ousted, may have used the political upheaval in Rome to attack and occupy the city himself, and use Rome as part of his own expanding political influence. This sort of warlordism was probably typical of politics in Italy at the time, and may explain much of the upheaval.
In essence, as a Mid to Late Republican specialist, and a military one at that, I struggle to intelligently summarise the very complex debate over what may have or may not have happened in Roman politics around the time Superbus was allegedly kicked out. However, I think can say that due to his central role in the literary tradition Superbus was more likely to have existed than to have not, and many of the broad details about him may be true, even the rape of Lucretia.* However, his role may have been exaggerated, and the political situation at Rome more complex and turbulent than reflected in the sources, due to other factors, such as the politicking of the nobiles and the rampant warlordism in Italy at the time.
Source: Cornell, The Beginnings of Rome, 1995.
*The rape of Lucretia I would be personally inclined to doubt, as it seems a fairly convenient, moralistic excuse for kicking the man out of his job, but Cornell seems to think it possible so I'll defer to him. I suppose it is the sort of thing that might make an aristocrat angry, and aristocrats (like Brutus et al.) were very much king-makers in Early Rome.