From 1919 to 1955 there was vehicle and pedestrian access from the Queensboro Bridge to Welfare (Roosevelt) Island. According to Neil Tandon writing for the Roosevelt Island Historical Society ( RIHS ):

… The Elevator Storehouse, opened in 1919, housed an elevator that
transported cars and people from the Queensboro Bridge down to the present-day
Tramway Plaza. In addition, it contained storage space and a reception ward
for the island’s Metropolitan Hospital. The building, whose main lobby was on
its top floor, was nicknamed the upside-down building and was featured in
Ripley’s Believe It or Not for its peculiar design. With the opening of the
Welfare Island Bridge, the building closed in 1955 and was demolished in
1970….


Image of Elevator Storehouse From Greater Astoria Historical Society

Today, the Roosevelt Island Connect Instagram page features Roosevelt Island Historical Society ( RIHS ) President Judy Berdy describing the Elevator Storehouse building.

According to the NYC Ambulance History Facebook Page:

The top floor of the Elevator Storehouse, as it was known, was a Reception
Hospital or ER, where patients were evaluated and treated before being put on
the elevator for transfer to one of three hospitals on the island: Metropolitan,
City or Island. The first two were relocated in the early 50s while the shell
of Island Hospital remains standing. The Elevator Storehouse served as the
central materials supply depot for the Department of Hospitals…. It was demolished to make way for the Roosevelt
Island Tram.

And:

The only legal way for pedestrians or bicyclists to get across the
Queensborough Bridge for a long time was. (starting at Manhattan side) take
the stairway at the south side of the bridge at 59th street to the upper_
level.

Then use the narrow walkway alongside the southern (eastward heading) roadway – which had lots of girders sticking through it… – _halfway_ across the bridge until you were over Welfare Island.

Then… another stairway sticking _out_ from that walkway, over the water, and leading to a passageway _under_ the lower level which took you over to the roof of the hospital building. (There might have been another stairway to get back up the flight).

Then… you’d go across the roof of the building to the elevator and be brought down to street level of the island…

In 2015 , Cornell Tech Assistant Director of Government & Community Affairs Jane Swanson reported that Cornell Tech raised the subject of pedestrian access from Roosevelt Island to the Queensboro Bridge with the NYC Department of Transportation during the Bloomberg administration in 2013, but at that time the Bloomberg administration was not interested in pursuing a feasibility study due to its scale, complexity and cost.

The 1962 TV Program Naked City episode titled Carrier , shown in the Instagram video, gives us a look at the Welfare (Roosevelt) Island staircase to the Queensboro Bridge.

Screenshot From You TubeAccording to the You Tube episode description:

After 14 years of self-imposed exile, a young woman who carries a deadly infectious disease leaves Welfare Island (now called Roosevelt Island) for Manhattan, alerting the NYPD to a potential plague.

Watch the full Naked City episode of Carrier. The Welfare (Roosevelt) Island scenes
are at the beginning and end.