The trials have begun several weeks late because of teething problems with the electric Class 385 train.
It is being tested overnight on the Gourock line in Inverclyde to avoid disrupting passenger services.
The four-carriage train is the first of 70 which will run on the main Edinburgh-Glasgow route and other lines across the Central Belt.
The initial problem is understood to have related to connecting the Hitachi train to a locomotive brought in for the tests.
A ScotRail Alliance spokesman said last month: "There’s an issue that’s being worked through at present and testing will commence when it’s resolved."
Programmes and transformation director Ian McConnell said: “It’s fantastic to have the first of our new trains actually running on Scotland’s railway as this means we are one step closer to making them available to our customers.
"But before we do that, we have to make sure each train is fully tested on the network.
"That means ensuring it interacts properly with railway infrastructure such as signals and overhead lines, and that’s what the team is focusing on.
"The train - codenamed T2 - is not yet fitted with seats and tables, so we’re using sandbags to represent their weight, as well as passengers.
"That means we are carrying out our tests in realistic conditions.
“Up next will be the second phase of testing, when the new fleet will be allowed to operate on the network alongside other trains.
That is likely to begin in spring on two routes from Edinburgh, to North Berwick and to Glasgow via Falkirk High.
Hitachi Rail project manager Andy Radford said: “ Hitachi’s trains have a reputation for their quality design and reliable running, so passengers will soon be feeling the benefits of trains that use leading Japanese technology and are built in the UK.”
All but the first ten of the fleet will be assembled by Hitachi Rail Europe at its new factory at Newton Aycliffe in County Durham.
By the end of next year, the trains will also run on the Edinburgh and Glasgow to Dunblane and Alloa lines, Glasgow-Cumbernauld/Falkirk Grahamston, Edinburgh-North Berwick/Dunbar/Berwick, Edinburgh-Glasgow via Shotts and Glasgow-Newton/Neilston/Cathcart Circle.