Probably not. The research that Reuters story was based on was later cited as using a potentially unreliable test that could have been affected by all of the subjects being older smokers.
As noted by Hilmar, Tumori Journal in Italy published Unexpected detection of SARS-CoV-2 antibodies in the prepandemic period in Italy, placing the earliest cases in Italy in September 2019. (Tumori Journal focuses on cancer, not epidemiology.)
This would be three months before the generally accepted first reports of the outbreak in China in December 2019 and four months before the first official reported case of Covid-19 in Italy from Jan. 3, 2020. There are some stories that talk about a Chinese patient who was sick in November 2019 who was later determined to have Covid-19, but the timing isn't clear, so it would be significant for Covid to be spreading in Italy months before it was noticed in China.
There is a comment on the original study from a group of Italian rheumatologists arguing that the method used by these cancer researchers to infer the presence of Covid-19 in earlier patients was flawed. They note that the data came from a study of 959 healthy smokers ages 55-65 across Italy who were enrolled in a cancer screening study. The serological tests detected the "presence of immunoglobulin M (IgM) and immunoglobulin G (IgG) antibodies to SARS-CoV-2." The rheumatologists note that, in short, smoking leads to an immunological reaction that generates false positives in this sort of testing and that the results should have been directly verified with molecular testing for the presence of Covid:
"Although serologic surveys are valuable tools for understanding public health, they can still suffer from some problems: they are indirect measures of the presence of the infection and do not have complete diagnostic reliability. The gold standard for diagnosing coronavirus disease 2019 (COVID-19) is molecular testing."
Addressing the criticisms and at the request of the World Health Organization, the original authors later had 29 original samples independently retested and published a followup in December 2021: Timeline of SARS-CoV-2 Spread in Italy: Results from an Independent Serological Retesting. That testing confirmed the earliest IGM-positive test as having been collected on Oct. 10, 2019. After some hypothesizing that a progenitor of Covid-19 may have spread in China much earlier than known and been carried to the industrial regions of Italy as early as June 2019, the authors acknowledge about their research: "the findings of these studies are only partially confirmed due to the heterogeneity of methods utilized and the risk of non-specific signals in serological assays."
In short, the evidence was suggestive, but the testing method was not conclusive.
Another study, A serological investigation in Southern Italy: was SARS-CoV-2 circulating in late 2019?, also says "these findings may indicate early circulation of SARS-CoV-2 in Apulia region in the autumn of 2019. However, it cannot be completely ruled out that the observed sero-reactivity could be an unknown antigen specificity in another virus to which subjects were exposed containing an epitope adventitiously cross-reactive with an epitope of SARS-CoV-2."
The possibility there being that a related SARS virus -- of which there may have been many -- or some Covid-19 precursor was in the environment, generating the same serological response without actually being Covid-19. (Which raises the question: If there was a virus like Covid-19 in the environment that wasn't spreading like Covid-19 and wasn't as lethal as Covid-19, can you say it was Covid-19?)