Tokyo has several lines like that, where a suburban line enters into the subway system.
The initial section of London's Metropoiltan Railway was intended to permit main line trains from Paddington to get closer to central London and also provide exchange with some of the other terminii being served. Later the Metropolitan and Great Western fell out and the Metropolitan responded by running its line as a standalone system, which over time developed into what is today the London Underground system.
The Elizabeth line is thus in a way a recreation of what already once was but is too crowded today to be able to accommodate its original purpose.
As mentioned by others on this thread, the Paris RER system is another good example of extending suburban rail lines into (and across) the city center. Although the RER was officially launched as such in the 1970s, the germinal section was the line from Gare d'Austerlitz to Gare d'Orsay which effectively already satisfied this function and was built to serve the Paris world exhibition of 1900.
In Barcelona the central interchange of Placa Catalunya began to take shape in the 1920s, when the interurban lines from Sarria that had previously accessed central Barcelona by sharing streetcar tracks, were placed into a tunnel, and an underground terminus built at Placa Catalunya. This line is today the backbone of the standard gauge part of the FGC system. At about the same time a broad gauge line was built to this location from the Arc de Triompf, initially intended for suburban trains but soon after integrated into the Barcelona metro (to this day line 1 is the only line of the Barcelona metro to be broad gauge, the other lines are all standard gauge). In the 1970s a new cross-city link serving this interchange was built for broad gauge suburban trains. Often overlooked is that this is not actually the first cross-city broad-gauge line as a couple of blocks away there is another line, serving Paseig de Gracia. This was initially surface running and opened in about 1901, but was moved into a tunnel in the 1950s to alleviate the nuisance to street traffic. This tunnel was for many years shared between suburban and long distance trains. With the recent opening of the high speed line (using a new tunnel a few blocks away) it now only sees suburban trains. For those interested in historical trivia, there was once a further cross-city line, running on the surface close to the sea front, serving mostly industries and the docks. The last remnants of this were dismantled to make way for facilities of the 1992 Olympics, but it had ceased to be relevant long before that.