The milestone came days before the world’s third oldest underground system celebrated its 125th birthday.
It is due to be followed by full-scale trials from April, with the trains expected to start carrying passengers in 2023.
They will replace trains that are now more than 40 years old as part of a £288.7 million overhaul of the 15-station circular railway.
The upgrade will enable services to run more frequently, with open plan walk-through interiors replacing separate carriages, and passengers able to see along tunnels from windows at each end of the trains.
They are scheduled to initially operate with drivers before switching to “unattended train operation” like some underground lines in Paris, Barcelona and Copenhagen.
Drivers will remain on board until platform safety screen doors are fitted at stations, similar to those on some London Underground lines.
Several other UK metro systems run without drivers, such as the Docklands Light Railway in London, but have on-board staff to operate the doors.
The trains may be introduced using existing Subway signalling while a new system is installed.
Subway operator Strathclyde Partnership for Transport’s (SPT) said the trial took place while the system was closed overnight on Saturday 4 December.
It was staged so the joint venture comprising Swiss train builders Stadler and signalling firm Hitachi could check the train could travel under its own power, running between the Subway’s Broomloan depot and nearby Govan station.
The train was also attached to one of the Subway’s “rescue” locomotives to check it could be retrieved in the event of a breakdown.
SPT described the exercises as “very successful” and said planning was underway to begin intensive overnight testing of the new trains in the Subway.
Subway director Antony Smith said: “I am delighted that these initial exercises, ahead of the in-system testing which is due to begin next year, went well.
"This has been an event long in the planning.
"It is an indication that things are moving forward again after a challenging year for the project with the impact of Covid and lockdowns, as well as the subsequent travel restrictions for our contractors.
“However, as 2021 comes to an end, getting the first train into the system is real progress and a sign that we can hope 2022 sees us get back on track with the modernisation programme.”
The first three of the 17 new trains have already been trialled on a surface test track between the Broomloan depot and near Ibrox stadium.
An SPT spokesperson said: “The joint venture has indicated that the next stage of intensive testing – before passenger service can commence – will take up to a year to complete, but we continue to press for the earliest possible completion to get the trains into service.”
The Subway, which is predated only by systems in London and Budapest, opened in 1896 and marked its 125th birthday on Tuesday with a new anniversary logo.