They said that studies show that all children younger than seven respond and develop better with play-based learning, while formal assessments in literacy and numeracy in the early years can put some children off learning.
The Liberal Democrats also support a later start to education and earlier this month led a debate on raising the school start age to seven.
The pointed to Finland, where education and child wellbeing outcomes are far higher than in Scotland, which the party said has in part been credited to their kindergarten system and primary school starting age of seven.
Scottish Greens co-leader Patrick Harvie said the plan could have a “vital role” in reducing the attainment gap.
He said: “The poverty related attainment gap in Scotland has persisted, and the clearest way to tackle this is by tackling poverty itself. That’s why the Scottish Greens have worked to deliver pandemic relief payments and ensured all primary pupils will get free school meals.
“The SNP were wrong to introduce standardised testing for primary ones, when international studies show younger children learn through play. The Scottish Greens believe Scotland should ditch the British model of starting school at four or five and instead look to our Scandinavian cousins.”
He added: “Finland is renowned for its education system, and it is recognised that kindergarten leads to better outcomes later in a child’s school career.”