I would suggest that the West Somerset Mineral Railway met the OP's criteria, at least in a "borderline" way. It opened in 1857, to bring iron ore from mines in the Brendon Hills to the sea at Watchet West Pier, for export; also ran a fairly small-time passenger service. The line was some 12 / 13 miles long. At its opening, it was totally isolated from the national rail network. Watchet acquired a connection to the national network a few years later: the branch (eventually GWR) from Taunton, opened in 1862; its extension to Minehead opened 1874. The Taunton -- Watchet -- Minehead branch, however, was not physically linked to the Mineral Railway -- no need for such a link was seen: the ore went out by sea. The Minehead branch crossed over the mineral line on a bridge, a little way west of the two lines' respective Watchet stations.
The Mineral Railway and its intimately-linked mining enterprise prospered less than their promoters had hoped; use lessened, and financial position worsened, in the late 19th century: in 1898, the whole undertaking was wound up and the railway closed completely. Track was not lifted; and a new company tried, in the period 1907 -- 10, to revive the mines and the railway -- using a fresh locomotive (a 4-4-0T purchased from the Metropolitan Railway), and fresh, though second-hand, goods stock. This venture failed, and ceased to function in 1910. The Mineral Railway had one last burst of semi-life in 1912 -- 14, in which its track between Watchet and the first station out, at Washford, was used by a company to experiment with its projected automatic signal warning device, employing two ex-GWR locos bought for the purpose. The line saw no further use after 1914.
Brief temporary connections were put in at Watchet, to get stock in and out for the two different projects described above; but essentially, the Mineral Railway did what it did in physical splendid isolation: no reason was perceived, to have a permanent link with the GWR line (the latter now, of course, the heritage West Somerset Railway).