I think not. Science fiction goes back MUCH farther than H.G. Wells. Remember Jules Verne?? And if you check lists of public domain sci-fi category books, you will find a fair number of other authors.
As worthy as Verne was, he was more a Belle Epoque adventure writer than an author trying to establish and promote a worldview as Welles was. Verne of course died before WWI laid waste to European civilization and made its shattered nations susceptible to Communism, with Welles becoming remarkably popular in that era in spite of his often heavy didacticism. The point though is not to mark the beginnings of sci fi but to identify Welles as a major influence on Heinlein.